Logics of Rational Agencyepacuit/lograt/nasslli2010/lograt-lec5a… · Logics of Rational Agency...
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Logics of Rational AgencyLecture 5
Eric Pacuit
Tilburg Institute for Logic and Philosophy of ScienceTilburg Univeristy
ai.stanford.edu/~epacuit
June 25, 2010
Eric Pacuit
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Questions
How should we represent and reason about the underlying protocol(or plans) that governs the agents’ interactions in a particularsocial situation?
1. What do agents “know” about the protocol, or plans?
2. Which dynamic operations change the protocol or plans overtime?
3. Logical issues: language design, axiomatization issues
Eric Pacuit
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Two Methodologies
ETL methodology: when describing a social situation, first writedown all possible sequences of events, then at each moment writedown the agents’ uncertainty, from that infer how the agents’knowledge changes from one moment to the next.
Alternative methodology: describe an initial situations, provide amethod for how events change a model that can be described inthe formal language, then construct the event tree as needed.
Dynamic Epistemic Logic
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Returning to the Example: DEL
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Returning to the Example: DEL
(M⊗ E1)⊗ E2
The initial model (Annand Bob are ignorantabout P2PM).
Private announcementto Ann about the talk.
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Returning to the Example: DEL
(M⊗ E1)⊗ E2
The initial model (Annand Bob are ignorantabout P2PM).
Private announcementto Ann about the talk.
Eric Pacuit
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Abstract Description of the Event
Recall the Ann and Bob example: Charles tells Bob that the talk isat 2PM.
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Abstract Description of the Event
Recall the Ann and Bob example: Charles tells Bob that the talk isat 2PM.
Pe1 P e2
>e3
B
BA
A
A, B
Ann knows which event took place.
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Abstract Description of the Event
Recall the Ann and Bob example: Charles tells Bob that the talk isat 2PM.
Pe1 P e2
>e3
B
BA
A
A, B
Ann knows which event took place.
Eric Pacuit
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Abstract Description of the Event
Recall the Ann and Bob example: Charles tells Bob that the talk isat 2PM.
Pe1 P e2
>e3
B
BA
A
A, B
Bob thinks a different event took place.
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Abstract Description of the Event
Recall the Ann and Bob example: Charles tells Bob that the talk isat 2PM.
Pe1 P e2
>e3
B
BA
A
A, B
That is, Bob learns the time of the talk, but Ann learns nothing.
Eric Pacuit
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Product Update
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Product Update
M⊗ E1
P
s
¬P
t
B
A, BA, B
E2
Pe1 P e2
>e3
B
BA
A
A, B
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Product Update
P
s
¬P
t
B
A, BA, B
Pe1 P e2
>e3
B
BA
A
A, B
P(s, e1) P (s, e2)
¬P (t, e3)P(s, e3)
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Product Update
P
s
¬P
t
B
A, BA, B
Pe1 P e2
>e3
B
BA
A
A, B
P(s, e1) P (s, e2)
¬P (t, e3)P(s, e3)
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Product Update
P
s
¬P
t
B
A, BA, B
Pe1 P e2
>e3
B
BA
A
A, B
(s, e1) |= ¬KBKAKBP P(s, e1) P (s, e2)
¬P (t, e3)P(s, e3)
Eric Pacuit
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Product Update
P
s
¬P
t
B
A, BA, B
Pe1 P e2
>e3
B
BA
A
A, B
(s, e1) |= ¬KBKAKBP P(s, e1) P (s, e2)
¬P (t, e3)P(s, e3)
B
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Product Update
P
s
¬P
t
B
A, BA, B
Pe1 P e2
>e3
B
BA
A
A, B
(s, e1) |= ¬KBKAKBP P(s, e1) P (s, e2)
¬P (t, e3)P(s, e3)
B
A
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Product Update
P
s
¬P
t
B
A, BB
Pe1 P e2
>e3
B
BA
A
A, B
(s, e1) |= ¬KBKAKBP P(s, e1) P (s, e2)
¬P (t, e3)P(s, e3)
B
A
B
Eric Pacuit
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Product Update Details
Let M = 〈W ,R,V 〉 be a Kripke model.
An event model is a tuple A = 〈A, S ,Pre〉, where S ⊆ A× A andPre : L → ℘(A).
The update model M⊗ A = 〈W ′,R ′,V ′〉 where
I W ′ = (w , a) | w |= Pre(a)I (w , a)R ′(w ′, a′) iff wRw ′ and aSa′
I (w , a) ∈ V (p) iff w ∈ V (p)
M,w |= [A, a]ϕ iff M,w |= Pre(a) implies M⊗ A, (w , a) |= ϕ.
Eric Pacuit
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Product Update Details
Let M = 〈W ,R,V 〉 be a Kripke model.
An event model is a tuple A = 〈A, S ,Pre〉, where S ⊆ A× A andPre : L → ℘(A).
The update model M⊗ A = 〈W ′,R ′,V ′〉 where
I W ′ = (w , a) | w |= Pre(a)I (w , a)R ′(w ′, a′) iff wRw ′ and aSa′
I (w , a) ∈ V (p) iff w ∈ V (p)
M,w |= [A, a]ϕ iff M,w |= Pre(a) implies M⊗ A, (w , a) |= ϕ.
Eric Pacuit
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Product Update Details
Let M = 〈W ,R,V 〉 be a Kripke model.
An event model is a tuple A = 〈A, S ,Pre〉, where S ⊆ A× A andPre : L → ℘(A).
The update model M⊗ A = 〈W ′,R ′,V ′〉 where
I W ′ = (w , a) | w |= Pre(a)
I (w , a)R ′(w ′, a′) iff wRw ′ and aSa′
I (w , a) ∈ V (p) iff w ∈ V (p)
M,w |= [A, a]ϕ iff M,w |= Pre(a) implies M⊗ A, (w , a) |= ϕ.
Eric Pacuit
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Product Update Details
Let M = 〈W ,R,V 〉 be a Kripke model.
An event model is a tuple A = 〈A, S ,Pre〉, where S ⊆ A× A andPre : L → ℘(A).
The update model M⊗ A = 〈W ′,R ′,V ′〉 where
I W ′ = (w , a) | w |= Pre(a)I (w , a)R ′(w ′, a′) iff wRw ′ and aSa′
I (w , a) ∈ V (p) iff w ∈ V (p)
M,w |= [A, a]ϕ iff M,w |= Pre(a) implies M⊗ A, (w , a) |= ϕ.
Eric Pacuit
![Page 24: Logics of Rational Agencyepacuit/lograt/nasslli2010/lograt-lec5a… · Logics of Rational Agency Lecture 5 Eric Pacuit Tilburg Institute for Logic and Philosophy of Science Tilburg](https://reader035.fdocuments.us/reader035/viewer/2022071410/6105aaf24d2ece0ae545431e/html5/thumbnails/24.jpg)
Product Update Details
Let M = 〈W ,R,V 〉 be a Kripke model.
An event model is a tuple A = 〈A, S ,Pre〉, where S ⊆ A× A andPre : L → ℘(A).
The update model M⊗ A = 〈W ′,R ′,V ′〉 where
I W ′ = (w , a) | w |= Pre(a)I (w , a)R ′(w ′, a′) iff wRw ′ and aSa′
I (w , a) ∈ V (p) iff w ∈ V (p)
M,w |= [A, a]ϕ iff M,w |= Pre(a) implies M⊗ A, (w , a) |= ϕ.
Eric Pacuit
![Page 25: Logics of Rational Agencyepacuit/lograt/nasslli2010/lograt-lec5a… · Logics of Rational Agency Lecture 5 Eric Pacuit Tilburg Institute for Logic and Philosophy of Science Tilburg](https://reader035.fdocuments.us/reader035/viewer/2022071410/6105aaf24d2ece0ae545431e/html5/thumbnails/25.jpg)
Product Update Details
Let M = 〈W ,R,V 〉 be a Kripke model.
An event model is a tuple A = 〈A, S ,Pre〉, where S ⊆ A× A andPre : L → ℘(A).
The update model M⊗ A = 〈W ′,R ′,V ′〉 where
I W ′ = (w , a) | w |= Pre(a)I (w , a)R ′(w ′, a′) iff wRw ′ and aSa′
I (w , a) ∈ V (p) iff w ∈ V (p)
M,w |= [A, a]ϕ iff M,w |= Pre(a) implies M⊗ A, (w , a) |= ϕ.
Eric Pacuit
![Page 26: Logics of Rational Agencyepacuit/lograt/nasslli2010/lograt-lec5a… · Logics of Rational Agency Lecture 5 Eric Pacuit Tilburg Institute for Logic and Philosophy of Science Tilburg](https://reader035.fdocuments.us/reader035/viewer/2022071410/6105aaf24d2ece0ae545431e/html5/thumbnails/26.jpg)
Literarture
A. Baltag and L. Moss. Logics for Epistemic Programs. 2004.
W. van der Hoek, H. van Ditmarsch and B. Kooi. Dynamic Episetmic Logic.2007.
Eric Pacuit
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DEL and ETL
Observation: By repeatedly updating an epistemic model withevent models, the machinery of DEL creates ETL models.
Let M be an epistemic model, and P a DEL protocol (tree of eventmodels). The ETL model generated by M and P, forest(M,P),represents all possible evolutions of the system obtained byupdating M with sequences from P.
Eric Pacuit
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DEL and ETL
Observation: By repeatedly updating an epistemic model withevent models, the machinery of DEL creates ETL models.
Let M be an epistemic model, and P a DEL protocol (tree of eventmodels). The ETL model generated by M and P, forest(M,P),represents all possible evolutions of the system obtained byupdating M with sequences from P.
Eric Pacuit
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Example: Initial Model and Protocol
P,Qs
P,Q,Rt P,R u
Q,R vi
i
i
j
j
j
!P
!Q !R
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Example
P, Qs
P, Q, Rt P, R u
Q, R vi
i
i
j
j
j
!P
!Q !R
(s, !P, !Q) (t, !P, !Q) (t, !P, !R) (u, !P, !R)
(s, !P)
(s) (t)
(t, !P)
(u)
(u, !P)
(v)
!P
!Q
!P
!Q !R
!P
!R
Eric Pacuit
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Example
P, Qs
P, Q, Rt P, R u
Q, R vi
i
i
j
j
j
!P
!Q !R
(s, !P, !Q) (t, !P, !Q) (t, !P, !R) (u, !P, !R)
(s, !P)
(s) (t)
(t, !P)
(u)
(u, !P)
(v)
!P
!Q
!P
!Q !R
!P
!R
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Example
P, Qs
P, Q, Rt P, R u
Q, R vi
i
i
j
j
j
!P
!Q !R
(s, !P, !Q) (t, !P, !Q) (t, !P, !R) (u, !P, !R)
(s, !P)
(s) (t)
(t, !P)
(u)
(u, !P)
(v)
!P
!Q
!P
!Q !R
!P
!R
Eric Pacuit
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Example
P, Qs
P, Q, Rt P, R u
Q, R vi
i
i
j
j
j
!P
!Q !R
(s, !P, !Q) (t, !P, !Q) (t, !P, !R) (u, !P, !R)
(s, !P)
(s) (t)
(t, !P)
(u)
(u, !P)
(v)
!P
!Q
!P
!Q !R
!P
!R
Eric Pacuit
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Example
P, Qs
P, Q, Rt P, R u
Q, R vi
i
i
j
j
j
!P
!Q !R
(s, !P, !Q) (t, !P, !Q) (t, !P, !R) (u, !P, !R)
(s, !P)
(s) (t)
(t, !P)
(u)
(u, !P)
(v)
!P
!Q
!P
!Q !R
!P
!R
Eric Pacuit
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Example
P, Qs
P, Q, Rt P, R u
Q, R vi
i
i
j
j
j
!P
!Q !R
(s, !P, !Q) (t, !P, !Q) (t, !P, !R) (u, !P, !R)
(s, !P)
(s) (t)
(t, !P)
(u)
(u, !P)
(v)
!P
!Q
!P
!Q !R
!P
!R
Eric Pacuit
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Example
P, Qs
P, Q, Rt P, R u
Q, R vi
i
i
j
j
j
!P
!Q !R
(s, !P, !Q) (t, !P, !Q) (t, !P, !R) (u, !P, !R)
(s, !P)
(s) (t)
(t, !P)
(u)
(u, !P)
(v)
!P
!Q
!P
!Q !R
!P
!R
Eric Pacuit
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Example
P, Qs
P, Q, Rt P, R u
Q, R vi
i
i
j
j
j
!P
!Q !R
(s, !P, !Q) (t, !P, !Q) (t, !P, !R) (u, !P, !R)
(s, !P)
(s) (t)
(t, !P)
(u)
(u, !P)
(v)
!P
!Q
!P
!Q !R
!P
!R
Eric Pacuit
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Example
P, Qs
P, Q, Rt P, R u
Q, R vi
i
i
j
j
j
!P
!Q !R
(s, !P, !Q) (t, !P, !Q) (t, !P, !R) (u, !P, !R)
(s, !P)
(s) (t)
(t, !P)
(u)
(u, !P)
(v)
!P
!Q
!P
!Q !R
!P
!R
(t) |= R ∧ ¬〈!R〉>
Eric Pacuit
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F(X) = Forest(M,P) | M an epistemic model and P ∈ X.
I Can we characterize the class of ETL models F(X)?
I Can we axiomatize interesting classes of DEL-generated ETLmodels?
J. van Benthem, J. Gerbrandy, T. Hoshi, EP. Merging Frameworks for Interaction.JPL, 2009.
Eric Pacuit
![Page 40: Logics of Rational Agencyepacuit/lograt/nasslli2010/lograt-lec5a… · Logics of Rational Agency Lecture 5 Eric Pacuit Tilburg Institute for Logic and Philosophy of Science Tilburg](https://reader035.fdocuments.us/reader035/viewer/2022071410/6105aaf24d2ece0ae545431e/html5/thumbnails/40.jpg)
A Characterization Theorem
Let Σ be a finite set of events and suppose XuniDEL is the class of
uniform DEL protocols (with a finiteness condition).
Characterization Theorem A model is in F(XuniDEL) iff it satisfies
propositional stability, synchronicity, perfect recall, local nomiracles, and local bisimulation invariance.
Eric Pacuit
![Page 41: Logics of Rational Agencyepacuit/lograt/nasslli2010/lograt-lec5a… · Logics of Rational Agency Lecture 5 Eric Pacuit Tilburg Institute for Logic and Philosophy of Science Tilburg](https://reader035.fdocuments.us/reader035/viewer/2022071410/6105aaf24d2ece0ae545431e/html5/thumbnails/41.jpg)
Constrained Public Announcement
1. A→ 〈A〉> vs. 〈A〉> → A
2. 〈A〉KiP ↔ A ∧ Ki 〈A〉P
3. 〈A〉KiP ↔ 〈A〉> ∧ Ki (A→ 〈A〉P)
4. 〈A〉KiP ↔ 〈A〉> ∧ Ki (〈A〉> → 〈A〉P)
Eric Pacuit
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Constrained Public Announcement
1. A→ 〈A〉> vs. 〈A〉> → A
2. 〈A〉KiP ↔ A ∧ Ki 〈A〉P
3. 〈A〉KiP ↔ 〈A〉> ∧ Ki (A→ 〈A〉P)
4. 〈A〉KiP ↔ 〈A〉> ∧ Ki (〈A〉> → 〈A〉P)
Eric Pacuit
![Page 43: Logics of Rational Agencyepacuit/lograt/nasslli2010/lograt-lec5a… · Logics of Rational Agency Lecture 5 Eric Pacuit Tilburg Institute for Logic and Philosophy of Science Tilburg](https://reader035.fdocuments.us/reader035/viewer/2022071410/6105aaf24d2ece0ae545431e/html5/thumbnails/43.jpg)
Constrained Public Announcement
1. A→ 〈A〉> vs. 〈A〉> → A
2. 〈A〉KiP ↔ A ∧ Ki 〈A〉P
3. 〈A〉KiP ↔ 〈A〉> ∧ Ki (A→ 〈A〉P)
4. 〈A〉KiP ↔ 〈A〉> ∧ Ki (〈A〉> → 〈A〉P)
Eric Pacuit
![Page 44: Logics of Rational Agencyepacuit/lograt/nasslli2010/lograt-lec5a… · Logics of Rational Agency Lecture 5 Eric Pacuit Tilburg Institute for Logic and Philosophy of Science Tilburg](https://reader035.fdocuments.us/reader035/viewer/2022071410/6105aaf24d2ece0ae545431e/html5/thumbnails/44.jpg)
Constrained Public Announcement
1. A→ 〈A〉> vs. 〈A〉> → A
2. 〈A〉KiP ↔ A ∧ Ki 〈A〉P
3. 〈A〉KiP ↔ 〈A〉> ∧ Ki (A→ 〈A〉P)
4. 〈A〉KiP ↔ 〈A〉> ∧ Ki (〈A〉> → 〈A〉P)
Eric Pacuit
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Questions
1. A public announcement is one specific type of event model,can we axiomatize classes of ETL models generated by othertypes of event models?
2. Which formal languages are best suited to describe these DELgenerated ETL models?
Eric Pacuit
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F(X) = Forest(M,P) | M an epistemic model and P ∈ X.
Examples: F(PAL), F(DEL), F(XPAL), F(XDEL), F(XSPriv ), . . .
Theorems. Sound and complete axiomatizations(Plaza, Gerbrandy, BMS, van Benthem et al., Hoshi & EP,Balibiani et al., Hoshi, . . .)
The logical playground: Decidability of MSO over trees (Rabin);combinations of PDL and S5; high undecidability just around thecorner (Halpern & Vardi, Miller & Moss)
J. van Benthem and EP. The Tree of Knowledge in Action. AiML 2006.
Eric Pacuit
![Page 47: Logics of Rational Agencyepacuit/lograt/nasslli2010/lograt-lec5a… · Logics of Rational Agency Lecture 5 Eric Pacuit Tilburg Institute for Logic and Philosophy of Science Tilburg](https://reader035.fdocuments.us/reader035/viewer/2022071410/6105aaf24d2ece0ae545431e/html5/thumbnails/47.jpg)
F(X) = Forest(M,P) | M an epistemic model and P ∈ X.
Examples: F(PAL), F(DEL), F(XPAL), F(XDEL), F(XSPriv ), . . .
Theorems. Sound and complete axiomatizations(Plaza, Gerbrandy, BMS, van Benthem et al., Hoshi & EP,Balibiani et al., Hoshi, . . .)
The logical playground: Decidability of MSO over trees (Rabin);combinations of PDL and S5; high undecidability just around thecorner (Halpern & Vardi, Miller & Moss)
J. van Benthem and EP. The Tree of Knowledge in Action. AiML 2006.
Eric Pacuit
![Page 48: Logics of Rational Agencyepacuit/lograt/nasslli2010/lograt-lec5a… · Logics of Rational Agency Lecture 5 Eric Pacuit Tilburg Institute for Logic and Philosophy of Science Tilburg](https://reader035.fdocuments.us/reader035/viewer/2022071410/6105aaf24d2ece0ae545431e/html5/thumbnails/48.jpg)
F(X) = Forest(M,P) | M an epistemic model and P ∈ X.
Examples: F(PAL), F(DEL), F(XPAL), F(XDEL), F(XSPriv ), . . .
Theorems. Sound and complete axiomatizations(Plaza, Gerbrandy, BMS, van Benthem et al., Hoshi & EP,Balibiani et al., Hoshi, . . .)
The logical playground: Decidability of MSO over trees (Rabin);combinations of PDL and S5; high undecidability just around thecorner (Halpern & Vardi, Miller & Moss)
J. van Benthem and EP. The Tree of Knowledge in Action. AiML 2006.
Eric Pacuit
![Page 49: Logics of Rational Agencyepacuit/lograt/nasslli2010/lograt-lec5a… · Logics of Rational Agency Lecture 5 Eric Pacuit Tilburg Institute for Logic and Philosophy of Science Tilburg](https://reader035.fdocuments.us/reader035/viewer/2022071410/6105aaf24d2ece0ae545431e/html5/thumbnails/49.jpg)
F(X) = Forest(M,P) | M an epistemic model and P ∈ X.
Examples: F(PAL), F(DEL), F(XPAL), F(XDEL), F(XSPriv ), . . .
Theorems. Sound and complete axiomatizations(Plaza, Gerbrandy, BMS, van Benthem et al., Hoshi & EP,Balibiani et al., Hoshi, . . .)
The logical playground: Decidability of MSO over trees (Rabin);combinations of PDL and S5; high undecidability just around thecorner (Halpern & Vardi, Miller & Moss)
J. van Benthem and EP. The Tree of Knowledge in Action. AiML 2006.
Eric Pacuit
![Page 50: Logics of Rational Agencyepacuit/lograt/nasslli2010/lograt-lec5a… · Logics of Rational Agency Lecture 5 Eric Pacuit Tilburg Institute for Logic and Philosophy of Science Tilburg](https://reader035.fdocuments.us/reader035/viewer/2022071410/6105aaf24d2ece0ae545431e/html5/thumbnails/50.jpg)
Returning to the original questions
How should we represent and reason about the underlying protocol(or plans) that governs the agents’ interactions in a particularsocial situation?
1. What do agents “know” about the protocol, or plans?
2. Which dynamic operations change the protocol or plans overtime?
3. Logical issues: language design, axiomatization issues
Eric Pacuit
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Returning to the original questions
How should we represent and reason about the underlying protocol(or plans) that governs the agents’ interactions in a particularsocial situation?
1. What do agents “know” about the protocol, or plans?
2. Which dynamic operations change the protocol or plans overtime?
3. Logical issues: language design, axiomatization issues
Eric Pacuit
![Page 52: Logics of Rational Agencyepacuit/lograt/nasslli2010/lograt-lec5a… · Logics of Rational Agency Lecture 5 Eric Pacuit Tilburg Institute for Logic and Philosophy of Science Tilburg](https://reader035.fdocuments.us/reader035/viewer/2022071410/6105aaf24d2ece0ae545431e/html5/thumbnails/52.jpg)
Returning to the original questions
How should we represent and reason about the underlying protocol(or plans) that governs the agents’ interactions in a particularsocial situation?
1. What do agents “know” about the protocol, or plans?
2. Which dynamic operations change the protocol or plans overtime?
3. Logical issues: language design, axiomatization issues
Eric Pacuit
![Page 53: Logics of Rational Agencyepacuit/lograt/nasslli2010/lograt-lec5a… · Logics of Rational Agency Lecture 5 Eric Pacuit Tilburg Institute for Logic and Philosophy of Science Tilburg](https://reader035.fdocuments.us/reader035/viewer/2022071410/6105aaf24d2ece0ae545431e/html5/thumbnails/53.jpg)
Returning to the original questions
How should we represent and reason about the underlying protocol(or plans) that governs the agents’ interactions in a particularsocial situation?
1. What do agents “know” about the protocol, or plans?
2. Which dynamic operations change the protocol or plans overtime?
3. Logical issues: language design, axiomatization issues
Eric Pacuit
![Page 54: Logics of Rational Agencyepacuit/lograt/nasslli2010/lograt-lec5a… · Logics of Rational Agency Lecture 5 Eric Pacuit Tilburg Institute for Logic and Philosophy of Science Tilburg](https://reader035.fdocuments.us/reader035/viewer/2022071410/6105aaf24d2ece0ae545431e/html5/thumbnails/54.jpg)
Returning to the original questions
How should we represent and reason about the underlying protocol(or plans) that governs the agents’ interactions in a particularsocial situation?
1. What do agents “know” about the protocol, or plans?
2. Which dynamic operations change the protocol or plans overtime?
3. Logical issues: language design, axiomatization issues
Eric Pacuit
![Page 55: Logics of Rational Agencyepacuit/lograt/nasslli2010/lograt-lec5a… · Logics of Rational Agency Lecture 5 Eric Pacuit Tilburg Institute for Logic and Philosophy of Science Tilburg](https://reader035.fdocuments.us/reader035/viewer/2022071410/6105aaf24d2ece0ae545431e/html5/thumbnails/55.jpg)
What is a Protocol?
Given the full tree T of events, a protocol is any subtree of T .
I A protocol is the set of histories compatible with someprocess, i.e., it is the “unwinding” of a (multi-agent) statetransition system.
I A protocol is the set of histories satisfying some property:
• Physical properties: every message is eventually answered, nomessage is received before it is sent
• Agent types: agent i is the type of agent who always lies,agent j is the type who always tells the truth
I A protocol is the set of histories of an extensive gameconsistent with a (partial) strategy profile.
Eric Pacuit
![Page 56: Logics of Rational Agencyepacuit/lograt/nasslli2010/lograt-lec5a… · Logics of Rational Agency Lecture 5 Eric Pacuit Tilburg Institute for Logic and Philosophy of Science Tilburg](https://reader035.fdocuments.us/reader035/viewer/2022071410/6105aaf24d2ece0ae545431e/html5/thumbnails/56.jpg)
What is a Protocol?
Given the full tree T of events, a protocol is any subtree of T .
I A protocol is the set of histories compatible with someprocess, i.e., it is the “unwinding” of a (multi-agent) statetransition system.
I A protocol is the set of histories satisfying some property:
• Physical properties: every message is eventually answered, nomessage is received before it is sent
• Agent types: agent i is the type of agent who always lies,agent j is the type who always tells the truth
I A protocol is the set of histories of an extensive gameconsistent with a (partial) strategy profile.
Eric Pacuit
![Page 57: Logics of Rational Agencyepacuit/lograt/nasslli2010/lograt-lec5a… · Logics of Rational Agency Lecture 5 Eric Pacuit Tilburg Institute for Logic and Philosophy of Science Tilburg](https://reader035.fdocuments.us/reader035/viewer/2022071410/6105aaf24d2ece0ae545431e/html5/thumbnails/57.jpg)
What is a Protocol?
Given the full tree T of events, a protocol is any subtree of T .
I A protocol is the set of histories compatible with someprocess, i.e., it is the “unwinding” of a (multi-agent) statetransition system.
I A protocol is the set of histories satisfying some property:
• Physical properties: every message is eventually answered, nomessage is received before it is sent
• Agent types: agent i is the type of agent who always lies,agent j is the type who always tells the truth
I A protocol is the set of histories of an extensive gameconsistent with a (partial) strategy profile.
Eric Pacuit
![Page 58: Logics of Rational Agencyepacuit/lograt/nasslli2010/lograt-lec5a… · Logics of Rational Agency Lecture 5 Eric Pacuit Tilburg Institute for Logic and Philosophy of Science Tilburg](https://reader035.fdocuments.us/reader035/viewer/2022071410/6105aaf24d2ece0ae545431e/html5/thumbnails/58.jpg)
What is a Protocol?
Given the full tree T of events, a protocol is any subtree of T .
I A protocol is the set of histories compatible with someprocess, i.e., it is the “unwinding” of a (multi-agent) statetransition system.
I A protocol is the set of histories satisfying some property:
• Physical properties: every message is eventually answered, nomessage is received before it is sent
• Agent types: agent i is the type of agent who always lies,agent j is the type who always tells the truth
I A protocol is the set of histories of an extensive gameconsistent with a (partial) strategy profile.
Eric Pacuit
![Page 59: Logics of Rational Agencyepacuit/lograt/nasslli2010/lograt-lec5a… · Logics of Rational Agency Lecture 5 Eric Pacuit Tilburg Institute for Logic and Philosophy of Science Tilburg](https://reader035.fdocuments.us/reader035/viewer/2022071410/6105aaf24d2ece0ae545431e/html5/thumbnails/59.jpg)
Reasoning about protocols, or plans
When can an agent agree to follow a protocol or plan?
What does the agent need to know about the protocol beforeagreeing to follow it?
EP and Sunil Simon. Reasoning with Protocols under Imperfect Information.manuscript.
Eric Pacuit
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Reasoning about protocols, or plans
When can an agent agree to follow a protocol or plan?
What does the agent need to know about the protocol beforeagreeing to follow it?
EP and Sunil Simon. Reasoning with Protocols under Imperfect Information.manuscript.
Eric Pacuit
![Page 61: Logics of Rational Agencyepacuit/lograt/nasslli2010/lograt-lec5a… · Logics of Rational Agency Lecture 5 Eric Pacuit Tilburg Institute for Logic and Philosophy of Science Tilburg](https://reader035.fdocuments.us/reader035/viewer/2022071410/6105aaf24d2ece0ae545431e/html5/thumbnails/61.jpg)
Arena
s0
s1 s2
s3 s4 s5
a b
c d c d
Eric Pacuit
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Protocol or PlanA protocol is a finite tree.
At s0, the agent agrees to either choose c or choose d :(a ∪ b); c ∪ (a ∪ b); d
s0
s1 s2
s3 s4 s5
a b
c d c d
Key idea: of course, PDL action expressions can encode any finitetree, but we want PDL over trees
Eric Pacuit
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Protocol or PlanA protocol is a finite tree.
At s0, the agent agrees to either choose c or choose d :(a ∪ b); c ∪ (a ∪ b); d
s0
s1 s2
s3 s4
a b
c c
-or-
s0
s1 s2
s4 s5
a b
d d
Key idea: of course, PDL action expressions can encode any finitetree, but we want PDL over trees
Eric Pacuit
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Protocol or Plan
A protocol is a finite tree.
At s0, the agent agrees to either choose c or choose d :(a ∪ b); c ∪ (a ∪ b); d
s0
s1 s2
s3 s4
a b
c c
-or-
s0
s1 s2
s4 s5
a b
d d
J. van Benthem. Logical Dynamics of Information and Interaction. CambridgeUniversity Press, 2010.
Eric Pacuit
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Protocol or PlanA protocol is a finite tree.
At s0, the agent agrees to either choose c or choose d :(a ∪ b); c ∪ (a ∪ b); d
s0
s1 s2
s3 s4
a b
c c
-or-
s0
s1 s2
s4 s5
a b
d d
Key idea: of course, PDL action expressions can encode any finitetree, but we want PDL over trees
Eric Pacuit
![Page 66: Logics of Rational Agencyepacuit/lograt/nasslli2010/lograt-lec5a… · Logics of Rational Agency Lecture 5 Eric Pacuit Tilburg Institute for Logic and Philosophy of Science Tilburg](https://reader035.fdocuments.us/reader035/viewer/2022071410/6105aaf24d2ece0ae545431e/html5/thumbnails/66.jpg)
Imperfect Information
The protocol is enabled:
s0
s1 s2
s3
a b
c d
a b
c d
Eric Pacuit
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Imperfect Information
The protocol is not enabled:
s0
s1 s2
s3
a b
c d
a b
c d
Eric Pacuit
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Protocols or Plans
A protocol is a finite tree T .
A complex protocol is generated by the following grammar:
T | π1;π2 | π1 ∪ π2 | π∗
Eric Pacuit
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Arena with Imperfect Information
An arena with imperfect information is a structureG I = (W , ⇒aa ∈ Σ, ) where ⊆W ×W .
For each position u in an arena, let I(u) = w | u w be theagent’s “point-of-view”.
For each u, let A(u) = v | ∃a ∈ Σ,w ⇒a v
Eric Pacuit
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Arena with Imperfect Information
I No Miracles: for all a ∈ Σ and all w , v ,w ′, v ′ ∈W , ifw v , w
a→w ′, and va→v ′, then w ′ v ′.
I Success: If w v then A(v) ⊆ A(w)
I Awareness: If w v then A(w) ⊆ A(v)
I Certainty of available actions: If w v and w v ′ thenA(v) = A(v ′)
Eric Pacuit
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Enabled
A protocol T is objectively enabled if T at u in an arena if Tcan be embedded in the unwinding of u.
A protocol T is subjectively enabled at a position u in an arenawith imperfect information if
1. the agent is certain that T is enabled (for all v ∈ I(u), T isenabled at v), and
2. the agent will be certain that she is in fact following theprotocol at every stage of the protocol.
Eric Pacuit
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Enabled
A protocol T is objectively enabled if T at u in an arena if Tcan be embedded in the unwinding of u.
A protocol T is subjectively enabled at a position u in an arenawith imperfect information if
1. the agent is certain that T is enabled (for all v ∈ I(u), T isenabled at v), and
2. the agent will be certain that she is in fact following theprotocol at every stage of the protocol.
Eric Pacuit
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Subjectively Enabled: The Idea
s0
s1 s2
s3 s4
a b
d c
s5
s6 s7
s9 s10s8
a b
d dc c
s11
s12 s13
c d
Eric Pacuit
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Adopting a Protocol
I Committing to a basic protocol T restricts the choicesavailable to the agent, but there is a trade-off: it alsoincreases the ability of the agent to guarantee that certainpropositions are true.
I Formally, each basic protocol (which is a finite tree) isassociated with a set of states X that the agent can “force”the situation to end up in by making choices consistent withthe protocol.
Eric Pacuit
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Adopting a Protocol
I Committing to a basic protocol T restricts the choicesavailable to the agent, but there is a trade-off: it alsoincreases the ability of the agent to guarantee that certainpropositions are true.
I Formally, each basic protocol (which is a finite tree) isassociated with a set of states X that the agent can “force”the situation to end up in by making choices consistent withthe protocol.
Eric Pacuit
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Adopting a Protocol
I There are a number of ways to make precise what it means foran agent to “guarantee” that some proposition is true becauseshe adopts the protocols T .
I Given a complex protocol π, the agent must first decide bothhow to go about adopting π then make her choices“in themoment” consistent with this plan. (Consider committing toT1 ∪ T2).
Eric Pacuit
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Adopting a Protocol
I There are a number of ways to make precise what it means foran agent to “guarantee” that some proposition is true becauseshe adopts the protocols T .
I Given a complex protocol π, the agent must first decide bothhow to go about adopting π then make her choices“in themoment” consistent with this plan. (Consider committing toT1 ∪ T2).
Eric Pacuit
![Page 78: Logics of Rational Agencyepacuit/lograt/nasslli2010/lograt-lec5a… · Logics of Rational Agency Lecture 5 Eric Pacuit Tilburg Institute for Logic and Philosophy of Science Tilburg](https://reader035.fdocuments.us/reader035/viewer/2022071410/6105aaf24d2ece0ae545431e/html5/thumbnails/78.jpg)
Reasoning about Abilities under Imperfect InformationKnowledge/belief:
I ϕ: “the agent has the information that ϕ is true”
Abilities:
I 〈π〉∀α: By adopting the protocol π, α is guaranteed to betrue.
I 〈π〉∃α: By adopting the protocol π, the agent can dosomething consistent with the protocol that will make α true.
“Epistemized” versions of the above operators:
I 〈π〉α: By agreeing to adopt the protocol π, the agent iscertain that α is guaranteed to be true.
I 〈π〉♦α: By agreeing to adopt the protocol π, the agent is can“knowingly” do something consistent with the protocol thatwill make α true.
Eric Pacuit
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Reasoning about Abilities under Imperfect InformationKnowledge/belief:
I M,w |= ϕ iff for all v , if w v then M, v |= ϕ.
Abilities:
I M, u |= 〈π〉∃α iff ∃(u,X ) ∈ R∃π , ∃w ∈ X such that M,w |= α.
I M, u |= 〈π〉∀α iff ∃(u,X ) ∈ R∀π such that ∀w ∈ X we haveM,w |= α.
“Epistemized” versions of the above operators:
I M, u |= 〈π〉α iff ∃(u,X ) ∈ Rπ such that ∀w ∈ X we haveM,w |= α.
I M, u |= 〈π〉♦α iff ∃(u,X ) ∈ R♦π such that ∀w ∈ X we haveM,w |= α.
Eric Pacuit
![Page 80: Logics of Rational Agencyepacuit/lograt/nasslli2010/lograt-lec5a… · Logics of Rational Agency Lecture 5 Eric Pacuit Tilburg Institute for Logic and Philosophy of Science Tilburg](https://reader035.fdocuments.us/reader035/viewer/2022071410/6105aaf24d2ece0ae545431e/html5/thumbnails/80.jpg)
Reasoning about Abilities under Imperfect InformationKnowledge/belief:
I M,w |= ϕ iff for all v , if w v then M, v |= ϕ.
Abilities:
I M, u |= 〈π〉∃α iff ∃(u,X ) ∈ R∃π , ∃w ∈ X such that M,w |= α.
I M, u |= 〈π〉∀α iff ∃(u,X ) ∈ R∀π such that ∀w ∈ X we haveM,w |= α.
“Epistemized” versions of the above operators:
I M, u |= 〈π〉α iff ∃(u,X ) ∈ Rπ such that ∀w ∈ X we haveM,w |= α.
I M, u |= 〈π〉♦α iff ∃(u,X ) ∈ R♦π such that ∀w ∈ X we haveM,w |= α.
Eric Pacuit
![Page 81: Logics of Rational Agencyepacuit/lograt/nasslli2010/lograt-lec5a… · Logics of Rational Agency Lecture 5 Eric Pacuit Tilburg Institute for Logic and Philosophy of Science Tilburg](https://reader035.fdocuments.us/reader035/viewer/2022071410/6105aaf24d2ece0ae545431e/html5/thumbnails/81.jpg)
Reasoning about Abilities under Imperfect InformationKnowledge/belief:
I M,w |= ϕ iff for all v , if w v then M, v |= ϕ.
Abilities:
I M, u |= 〈π〉∃α iff ∃(u,X ) ∈ R∃π , ∃w ∈ X such that M,w |= α.
I M, u |= 〈π〉∀α iff ∃(u,X ) ∈ R∀π such that ∀w ∈ X we haveM,w |= α.
“Epistemized” versions of the above operators:
I M, u |= 〈π〉α iff ∃(u,X ) ∈ Rπ such that ∀w ∈ X we haveM,w |= α.
I M, u |= 〈π〉♦α iff ∃(u,X ) ∈ R♦π such that ∀w ∈ X we haveM,w |= α.
Eric Pacuit
![Page 82: Logics of Rational Agencyepacuit/lograt/nasslli2010/lograt-lec5a… · Logics of Rational Agency Lecture 5 Eric Pacuit Tilburg Institute for Logic and Philosophy of Science Tilburg](https://reader035.fdocuments.us/reader035/viewer/2022071410/6105aaf24d2ece0ae545431e/html5/thumbnails/82.jpg)
Reasoning about Abilities under Imperfect Information
I RFt = (u,X ) | enabled(Tt , u) and frontier(Tu |\ Tt)) = X
(for F ∈ ∃,∀).
I Rt = (u,X ) | s-enabled(Tt , u) and frontier((G, u) |\s Tt)) =X.
I R♦t = (u,X ) | s-enabled(Tt , u) and ∃ρ ∈Paths(Tt) with S(ρ, u) = Z0Z1 . . .Zk and X = last(Zk).
Eric Pacuit
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Logics of Information and Abilities
I Combining PDL with epistemic/doxastic logics
R. Schmidt and D. Tishkovsky. On combinations of propositional dynamic logicand doxastic modal logics. JOLLI, 2008.
I Knowing how to execute a plan/win a game
A. Herzig and N. Troquard. Knowing how to play: uniform choices in logics ofagency. Proceedings of AAMAS 2006, pgs. 209 - 216.
Y. Lesperance, H. Levesque, F. Lin and R. Scherl. Ability and Knowing How inthe Situation Calculus. Studia Logica 65, pgs. 165 - 186, 2000.
EP and S. Simon. Reasoning about protocols under imperfect information.manuscript, 2010.
Eric Pacuit
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Logics of Information and Abilities
I Combining PDL with epistemic/doxastic logics
R. Schmidt and D. Tishkovsky. On combinations of propositional dynamic logicand doxastic modal logics. JOLLI, 2008.
I Knowing how to execute a plan/win a game
A. Herzig and N. Troquard. Knowing how to play: uniform choices in logics ofagency. Proceedings of AAMAS 2006, pgs. 209 - 216.
Y. Lesperance, H. Levesque, F. Lin and R. Scherl. Ability and Knowing How inthe Situation Calculus. Studia Logica 65, pgs. 165 - 186, 2000.
EP and S. Simon. Reasoning about protocols under imperfect information.manuscript, 2010.
Eric Pacuit
![Page 85: Logics of Rational Agencyepacuit/lograt/nasslli2010/lograt-lec5a… · Logics of Rational Agency Lecture 5 Eric Pacuit Tilburg Institute for Logic and Philosophy of Science Tilburg](https://reader035.fdocuments.us/reader035/viewer/2022071410/6105aaf24d2ece0ae545431e/html5/thumbnails/85.jpg)
Merging Logics of Rational Agency
X Entangling Knowledge/Beliefs and Preferences
X Reasoning with protocols
X “Epistemizing” Logics of Action and Ability: knowing how toachieve ϕ vs. knowing that you can achieve ϕ
I Plans Change (dynamic BDI - belief desire intention - logics)
Eric Pacuit
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The Revision Problem
State ∗ Input = State ′
What about other aspects of rational agency?
How should we describe the “mental state”?Propositional formulas
What is a coherent description?A belief state is a consistent and deductively closed set ofpropositional formulas
What are the inputs?Consistent propositional formula
How should we characterize the revision operator?AGM postulates, Dynamic Doxastic Logic
Eric Pacuit
![Page 87: Logics of Rational Agencyepacuit/lograt/nasslli2010/lograt-lec5a… · Logics of Rational Agency Lecture 5 Eric Pacuit Tilburg Institute for Logic and Philosophy of Science Tilburg](https://reader035.fdocuments.us/reader035/viewer/2022071410/6105aaf24d2ece0ae545431e/html5/thumbnails/87.jpg)
The Revision Problem
State ∗ Input = State ′
What about other aspects of rational agency?
1. How should we describe the “mental state”?Propositional formulas
2. What is a coherent description?A belief state is a consistent and deductively closed set ofpropositional formulas
3. What are the inputs?Consistent propositional formula
4. How should we characterize the revision operator?AGM postulates, Dynamic Doxastic Logic
Eric Pacuit
![Page 88: Logics of Rational Agencyepacuit/lograt/nasslli2010/lograt-lec5a… · Logics of Rational Agency Lecture 5 Eric Pacuit Tilburg Institute for Logic and Philosophy of Science Tilburg](https://reader035.fdocuments.us/reader035/viewer/2022071410/6105aaf24d2ece0ae545431e/html5/thumbnails/88.jpg)
The Revision Problem
State ∗ Input = State ′
What about other aspects of rational agency?
1. How should we describe the “mental state”?Propositional formulas
2. What is a coherent description?A belief state is a consistent and deductively closed set ofpropositional formulas
3. What are the inputs?Consistent propositional formula
4. How should we characterize the revision operator?AGM postulates, Dynamic Doxastic Logic
Eric Pacuit
![Page 89: Logics of Rational Agencyepacuit/lograt/nasslli2010/lograt-lec5a… · Logics of Rational Agency Lecture 5 Eric Pacuit Tilburg Institute for Logic and Philosophy of Science Tilburg](https://reader035.fdocuments.us/reader035/viewer/2022071410/6105aaf24d2ece0ae545431e/html5/thumbnails/89.jpg)
The Revision Problem
State ∗ Input = State ′
What about other aspects of rational agency?
1. How should we describe the “mental state”?Propositional formulas
2. What is a coherent description?A belief state is a consistent and deductively closed set ofpropositional formulas
3. What are the inputs?Consistent propositional formula
4. How should we characterize the revision operator?AGM postulates, Dynamic Doxastic Logic
Eric Pacuit
![Page 90: Logics of Rational Agencyepacuit/lograt/nasslli2010/lograt-lec5a… · Logics of Rational Agency Lecture 5 Eric Pacuit Tilburg Institute for Logic and Philosophy of Science Tilburg](https://reader035.fdocuments.us/reader035/viewer/2022071410/6105aaf24d2ece0ae545431e/html5/thumbnails/90.jpg)
The Revision Problem
State ∗ Input = State ′
What about other aspects of rational agency?
1. How should we describe the “mental state”?Propositional formulas
2. What is a coherent description?A belief state is a consistent and deductively closed set ofpropositional formulas
3. What are the inputs?Consistent propositional formula
4. How should we characterize the revision operator?AGM postulates, Dynamic Doxastic Logic
Eric Pacuit
![Page 91: Logics of Rational Agencyepacuit/lograt/nasslli2010/lograt-lec5a… · Logics of Rational Agency Lecture 5 Eric Pacuit Tilburg Institute for Logic and Philosophy of Science Tilburg](https://reader035.fdocuments.us/reader035/viewer/2022071410/6105aaf24d2ece0ae545431e/html5/thumbnails/91.jpg)
The Revision Problem
B ∗ ϕ = B′
What about other aspects of rational agency?
1. How should we describe the “mental state”?Propositional formulas
2. What is a coherent description?A belief state is a consistent and deductively closed set ofpropositional formulas
3. What are the inputs?Consistent propositional formula, other belief sets
4. How should we characterize the revision operator?AGM postulates, Dynamic Doxastic Logic
Eric Pacuit
![Page 92: Logics of Rational Agencyepacuit/lograt/nasslli2010/lograt-lec5a… · Logics of Rational Agency Lecture 5 Eric Pacuit Tilburg Institute for Logic and Philosophy of Science Tilburg](https://reader035.fdocuments.us/reader035/viewer/2022071410/6105aaf24d2ece0ae545431e/html5/thumbnails/92.jpg)
The Revision Problem
State ∗ Input = State ′
What about other aspects of rational agency?
1. How should we describe the “mental state”?Propositional formulas
2. What is a coherent description?A belief state is a consistent and deductively closed set ofpropositional formulas
3. What are the inputs?Consistent propositional formula, other belief sets
4. How should we characterize the revision operator?AGM postulates, Dynamic Doxastic Logic
Eric Pacuit
![Page 93: Logics of Rational Agencyepacuit/lograt/nasslli2010/lograt-lec5a… · Logics of Rational Agency Lecture 5 Eric Pacuit Tilburg Institute for Logic and Philosophy of Science Tilburg](https://reader035.fdocuments.us/reader035/viewer/2022071410/6105aaf24d2ece0ae545431e/html5/thumbnails/93.jpg)
Revising Mental Attitudes
X Preference change
T. Grune-Yanoff and S. Ove Hansen (eds.). Preference Change. Vol. 42, Theoryand Decision Library (2009).
X General model of “attitude” change
C. List and F. Dietrich. The aggregation of propositional attitudes: towards ageneral theory. Oxford Studies in Epistemology 3 (forthcoming).
X Goal dynamics
C. Castelgranchi and F. Paglieri. The role of beliefs in goal dynamics: Prole-gomena to a constructive theory of intentions. Synthese 155: 237 - 263 (2007).
Today: Intention dynamics
Eric Pacuit
![Page 94: Logics of Rational Agencyepacuit/lograt/nasslli2010/lograt-lec5a… · Logics of Rational Agency Lecture 5 Eric Pacuit Tilburg Institute for Logic and Philosophy of Science Tilburg](https://reader035.fdocuments.us/reader035/viewer/2022071410/6105aaf24d2ece0ae545431e/html5/thumbnails/94.jpg)
Revising Mental Attitudes
X Preference change
T. Grune-Yanoff and S. Ove Hansen (eds.). Preference Change. Vol. 42, Theoryand Decision Library (2009).
X General model of “attitude” change
C. List and F. Dietrich. The aggregation of propositional attitudes: towards ageneral theory. Oxford Studies in Epistemology 3 (forthcoming).
X Goal dynamics
C. Castelgranchi and F. Paglieri. The role of beliefs in goal dynamics: Prole-gomena to a constructive theory of intentions. Synthese 155: 237 - 263 (2007).
Today: Intention dynamics
Eric Pacuit
![Page 95: Logics of Rational Agencyepacuit/lograt/nasslli2010/lograt-lec5a… · Logics of Rational Agency Lecture 5 Eric Pacuit Tilburg Institute for Logic and Philosophy of Science Tilburg](https://reader035.fdocuments.us/reader035/viewer/2022071410/6105aaf24d2ece0ae545431e/html5/thumbnails/95.jpg)
Revising Mental Attitudes
X Preference change
T. Grune-Yanoff and S. Ove Hansen (eds.). Preference Change. Vol. 42, Theoryand Decision Library (2009).
X General model of “attitude” change
C. List and F. Dietrich. The aggregation of propositional attitudes: towards ageneral theory. Oxford Studies in Epistemology 3 (forthcoming).
X Goal dynamics
C. Castelgranchi and F. Paglieri. The role of beliefs in goal dynamics: Prole-gomena to a constructive theory of intentions. Synthese 155: 237 - 263 (2007).
Today: Intention dynamics
Eric Pacuit
![Page 96: Logics of Rational Agencyepacuit/lograt/nasslli2010/lograt-lec5a… · Logics of Rational Agency Lecture 5 Eric Pacuit Tilburg Institute for Logic and Philosophy of Science Tilburg](https://reader035.fdocuments.us/reader035/viewer/2022071410/6105aaf24d2ece0ae545431e/html5/thumbnails/96.jpg)
Revising Mental Attitudes
X Preference change
T. Grune-Yanoff and S. Ove Hansen (eds.). Preference Change. Vol. 42, Theoryand Decision Library (2009).
X General model of “attitude” change
C. List and F. Dietrich. The aggregation of propositional attitudes: towards ageneral theory. Oxford Studies in Epistemology 3 (forthcoming).
X Goal dynamics
C. Castelgranchi and F. Paglieri. The role of beliefs in goal dynamics: Prole-gomena to a constructive theory of intentions. Synthese 155: 237 - 263 (2007).
Today: Intention dynamics
Eric Pacuit
![Page 97: Logics of Rational Agencyepacuit/lograt/nasslli2010/lograt-lec5a… · Logics of Rational Agency Lecture 5 Eric Pacuit Tilburg Institute for Logic and Philosophy of Science Tilburg](https://reader035.fdocuments.us/reader035/viewer/2022071410/6105aaf24d2ece0ae545431e/html5/thumbnails/97.jpg)
Conceptual Background: Intentions
Important distinctions:
1. (Present-directed) The intention with which someone acts
2. (Present-directed) Intentional action
3. (Future-directed) Intending to do some action
Some issues:
Unifying account of intentions
“Where we are tempted to speak of ‘different senses’ of aword which is clearly not equivocal, we may infer that we arepretty much in the dark about the character of the conceptwhich it represents”- G.E.M. Anscombe, Intention, pg. 1
Eric Pacuit
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Conceptual Background: Intentions
Important distinctions:
1. (Present-directed) The intention with which someone acts
2. (Present-directed) Intentional action
3. (Future-directed) Intending to do some action
Some issues:
I Unifying account of intentions
“Where we are tempted to speak of ‘different senses’ of aword which is clearly not equivocal, we may infer that we arepretty much in the dark about the character of the conceptwhich it represents”- G.E.M. Anscombe, Intention, pg. 1
Eric Pacuit
![Page 99: Logics of Rational Agencyepacuit/lograt/nasslli2010/lograt-lec5a… · Logics of Rational Agency Lecture 5 Eric Pacuit Tilburg Institute for Logic and Philosophy of Science Tilburg](https://reader035.fdocuments.us/reader035/viewer/2022071410/6105aaf24d2ece0ae545431e/html5/thumbnails/99.jpg)
Conceptual Background: Intentions
Important distinctions:
1. (Present-directed) The intention with which someone acts
2. (Present-directed) Intentional action
3. (Future-directed) Intending to do some action
Some issues:
I Unifying account of intentions
I Intention as a mental state
pro-attitude (vs. informational attitude), world-to-minddirection of fit, conduct-controlling
Eric Pacuit
![Page 100: Logics of Rational Agencyepacuit/lograt/nasslli2010/lograt-lec5a… · Logics of Rational Agency Lecture 5 Eric Pacuit Tilburg Institute for Logic and Philosophy of Science Tilburg](https://reader035.fdocuments.us/reader035/viewer/2022071410/6105aaf24d2ece0ae545431e/html5/thumbnails/100.jpg)
Conceptual Background: Intentions
Important distinctions:
1. (Present-directed) The intention with which someone acts2. (Present-directed) Intentional action3. (Future-directed) Intending to do some action
Some issues:
I Unifying account of intentionsI Intention as a mental stateI Intentions are (always) directed towards actions
“Although we sometimes report intention as a propositionalattitude — ‘I intend that p’ — such reports can always berecast as ‘intending to ....’ as when I intend to bring aboutthat p. By contrast, it is difficult to rephrase such mundaneexpressions as ‘I intend to walk home’ in propositional terms”
Eric Pacuit
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Conceptual Background: Intentions
Important distinctions:
1. (Present-directed) The intention with which someone acts
2. (Present-directed) Intentional action
3. (Future-directed) Intending to do some action
Some issues:
I Unifying account of intentions
I Intention as a mental state
I Intentions are (always) directed towards actions
An extensive literature:
K. Setiya. Intention. Stanford Encyclopedia of Philosophy (2010).
Eric Pacuit
![Page 102: Logics of Rational Agencyepacuit/lograt/nasslli2010/lograt-lec5a… · Logics of Rational Agency Lecture 5 Eric Pacuit Tilburg Institute for Logic and Philosophy of Science Tilburg](https://reader035.fdocuments.us/reader035/viewer/2022071410/6105aaf24d2ece0ae545431e/html5/thumbnails/102.jpg)
Conceptual Background: Intentions
Important distinctions:
1. (Present-directed) The intention with which someone acts
2. (Present-directed) Intentional action
3. (Future-directed) Intending to do some action
Some issues:
I Unifying account of intentions
I Intention as a mental state
I Intentions are (always) directed towards actions
An extensive literature:
K. Setiya. Intention. Stanford Encyclopedia of Philosophy (2010).
Eric Pacuit
![Page 103: Logics of Rational Agencyepacuit/lograt/nasslli2010/lograt-lec5a… · Logics of Rational Agency Lecture 5 Eric Pacuit Tilburg Institute for Logic and Philosophy of Science Tilburg](https://reader035.fdocuments.us/reader035/viewer/2022071410/6105aaf24d2ece0ae545431e/html5/thumbnails/103.jpg)
Functional Description of IntentionsM. Bratman. Intentions, Plans and Practical Reason. Harvard University Press(1987).
“intention is a distinctive practical attitude marked by its pivotalrole in planning for the future.
Intention involves desire, but evenpredominant desire is insufficient for intention, since it need notinvolve a commitment to act: intentions are conduct-controllingpro-attitudes, ones which we are disposed to retain withoutreconsideration, and which play a significant role as inputs to[means-end] reasoning” (pg. 20)
Eric Pacuit
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Functional Description of IntentionsM. Bratman. Intentions, Plans and Practical Reason. Harvard University Press(1987).
“intention is a distinctive practical attitude marked by its pivotalrole in planning for the future. Intention involves desire, but evenpredominant desire is insufficient for intention, since it need notinvolve a commitment to act:
intentions are conduct-controllingpro-attitudes, ones which we are disposed to retain withoutreconsideration, and which play a significant role as inputs to[means-end] reasoning” (pg. 20)
Eric Pacuit
![Page 105: Logics of Rational Agencyepacuit/lograt/nasslli2010/lograt-lec5a… · Logics of Rational Agency Lecture 5 Eric Pacuit Tilburg Institute for Logic and Philosophy of Science Tilburg](https://reader035.fdocuments.us/reader035/viewer/2022071410/6105aaf24d2ece0ae545431e/html5/thumbnails/105.jpg)
Functional Description of IntentionsM. Bratman. Intentions, Plans and Practical Reason. Harvard University Press(1987).
“intention is a distinctive practical attitude marked by its pivotalrole in planning for the future. Intention involves desire, but evenpredominant desire is insufficient for intention, since it need notinvolve a commitment to act: intentions are conduct-controllingpro-attitudes, ones which we are disposed to retain withoutreconsideration, and which play a significant role as inputs to[means-end] reasoning” (pg. 20)
Eric Pacuit
![Page 106: Logics of Rational Agencyepacuit/lograt/nasslli2010/lograt-lec5a… · Logics of Rational Agency Lecture 5 Eric Pacuit Tilburg Institute for Logic and Philosophy of Science Tilburg](https://reader035.fdocuments.us/reader035/viewer/2022071410/6105aaf24d2ece0ae545431e/html5/thumbnails/106.jpg)
Functional Description of IntentionsM. Bratman. Intentions, Plans and Practical Reason. Harvard University Press(1987).
Committing to an action in advance is crucial for
1. our capacity to make rational decisions (as a bounded agent)
2. our capacity to engage in complex, temporally extendedprojects
3. our capacity to coordinate with others
Of course, this commitment is defeasible...
Eric Pacuit
![Page 107: Logics of Rational Agencyepacuit/lograt/nasslli2010/lograt-lec5a… · Logics of Rational Agency Lecture 5 Eric Pacuit Tilburg Institute for Logic and Philosophy of Science Tilburg](https://reader035.fdocuments.us/reader035/viewer/2022071410/6105aaf24d2ece0ae545431e/html5/thumbnails/107.jpg)
Functional Description of IntentionsM. Bratman. Intentions, Plans and Practical Reason. Harvard University Press(1987).
Committing to an action in advance is crucial for
1. our capacity to make rational decisions (as a bounded agent)
2. our capacity to engage in complex, temporally extendedprojects
3. our capacity to coordinate with others
Of course, this commitment is defeasible...
Eric Pacuit
![Page 108: Logics of Rational Agencyepacuit/lograt/nasslli2010/lograt-lec5a… · Logics of Rational Agency Lecture 5 Eric Pacuit Tilburg Institute for Logic and Philosophy of Science Tilburg](https://reader035.fdocuments.us/reader035/viewer/2022071410/6105aaf24d2ece0ae545431e/html5/thumbnails/108.jpg)
Functional Description of IntentionsM. Bratman. Intentions, Plans and Practical Reason. Harvard University Press(1987).
Committing to an action in advance is crucial for
1. our capacity to make rational decisions (as a bounded agent)
2. our capacity to engage in complex, temporally extendedprojects
3. our capacity to coordinate with others
Of course, this commitment is defeasible...
Eric Pacuit
![Page 109: Logics of Rational Agencyepacuit/lograt/nasslli2010/lograt-lec5a… · Logics of Rational Agency Lecture 5 Eric Pacuit Tilburg Institute for Logic and Philosophy of Science Tilburg](https://reader035.fdocuments.us/reader035/viewer/2022071410/6105aaf24d2ece0ae545431e/html5/thumbnails/109.jpg)
Functional Description of IntentionsM. Bratman. Intentions, Plans and Practical Reason. Harvard University Press(1987).
Committing to an action in advance is crucial for
1. our capacity to make rational decisions (as a bounded agent)
2. our capacity to engage in complex, temporally extendedprojects
3. our capacity to coordinate with others
Of course, this commitment is defeasible...
Eric Pacuit
![Page 110: Logics of Rational Agencyepacuit/lograt/nasslli2010/lograt-lec5a… · Logics of Rational Agency Lecture 5 Eric Pacuit Tilburg Institute for Logic and Philosophy of Science Tilburg](https://reader035.fdocuments.us/reader035/viewer/2022071410/6105aaf24d2ece0ae545431e/html5/thumbnails/110.jpg)
Functional Description of IntentionsM. Bratman. Intentions, Plans and Practical Reason. Harvard University Press(1987).
Committing to an action in advance is crucial for
1. our capacity to make rational decisions (as a bounded agent)
2. our capacity to engage in complex, temporally extendedprojects
3. our capacity to coordinate with others
Of course, this commitment is defeasible...
Eric Pacuit
![Page 111: Logics of Rational Agencyepacuit/lograt/nasslli2010/lograt-lec5a… · Logics of Rational Agency Lecture 5 Eric Pacuit Tilburg Institute for Logic and Philosophy of Science Tilburg](https://reader035.fdocuments.us/reader035/viewer/2022071410/6105aaf24d2ece0ae545431e/html5/thumbnails/111.jpg)
Stability of PlansM. Bratman. Intentions, Plans and Practical Reason. Harvard University Press(1987).
plans normally resist reconsideration:
“an agent’s habits anddispositions concerning the reconsideration or nonreconsiderationof a prior intention or plan determine the stability of that intentionor plan”. .... “The stability of [the agent’s] plans will generally notbe an isolated feature of those plans but will be linked to otherfeatures of [the agent’s] psychology” (pg. 65)
What happens in “abnormal” or “surprising” situations? Thispoints to a theory of (rational) intention/plan revision...
Eric Pacuit
![Page 112: Logics of Rational Agencyepacuit/lograt/nasslli2010/lograt-lec5a… · Logics of Rational Agency Lecture 5 Eric Pacuit Tilburg Institute for Logic and Philosophy of Science Tilburg](https://reader035.fdocuments.us/reader035/viewer/2022071410/6105aaf24d2ece0ae545431e/html5/thumbnails/112.jpg)
Stability of PlansM. Bratman. Intentions, Plans and Practical Reason. Harvard University Press(1987).
plans normally resist reconsideration: “an agent’s habits anddispositions concerning the reconsideration or nonreconsiderationof a prior intention or plan determine the stability of that intentionor plan”.
.... “The stability of [the agent’s] plans will generally notbe an isolated feature of those plans but will be linked to otherfeatures of [the agent’s] psychology” (pg. 65)
What happens in “abnormal” or “surprising” situations? Thispoints to a theory of (rational) intention/plan revision...
Eric Pacuit
![Page 113: Logics of Rational Agencyepacuit/lograt/nasslli2010/lograt-lec5a… · Logics of Rational Agency Lecture 5 Eric Pacuit Tilburg Institute for Logic and Philosophy of Science Tilburg](https://reader035.fdocuments.us/reader035/viewer/2022071410/6105aaf24d2ece0ae545431e/html5/thumbnails/113.jpg)
Stability of PlansM. Bratman. Intentions, Plans and Practical Reason. Harvard University Press(1987).
plans normally resist reconsideration: “an agent’s habits anddispositions concerning the reconsideration or nonreconsiderationof a prior intention or plan determine the stability of that intentionor plan”. .... “The stability of [the agent’s] plans will generally notbe an isolated feature of those plans but will be linked to otherfeatures of [the agent’s] psychology” (pg. 65)
What happens in “abnormal” or “surprising” situations? Thispoints to a theory of (rational) intention/plan revision...
Eric Pacuit
![Page 114: Logics of Rational Agencyepacuit/lograt/nasslli2010/lograt-lec5a… · Logics of Rational Agency Lecture 5 Eric Pacuit Tilburg Institute for Logic and Philosophy of Science Tilburg](https://reader035.fdocuments.us/reader035/viewer/2022071410/6105aaf24d2ece0ae545431e/html5/thumbnails/114.jpg)
Stability of PlansM. Bratman. Intentions, Plans and Practical Reason. Harvard University Press(1987).
plans normally resist reconsideration: “an agent’s habits anddispositions concerning the reconsideration or nonreconsiderationof a prior intention or plan determine the stability of that intentionor plan”. .... “The stability of [the agent’s] plans will generally notbe an isolated feature of those plans but will be linked to otherfeatures of [the agent’s] psychology” (pg. 65)
What happens in “abnormal” or “surprising” situations? Thispoints to a theory of (rational) intention/plan revision...
Eric Pacuit
![Page 115: Logics of Rational Agencyepacuit/lograt/nasslli2010/lograt-lec5a… · Logics of Rational Agency Lecture 5 Eric Pacuit Tilburg Institute for Logic and Philosophy of Science Tilburg](https://reader035.fdocuments.us/reader035/viewer/2022071410/6105aaf24d2ece0ae545431e/html5/thumbnails/115.jpg)
Conceptual Issue: intentions and beliefs are entangled
Intending to act just is a special kind of belief that one will;
Intending to act involves a belief that one will so act;
Intending to act involve a belief that it is possible that onewill so act.
Eric Pacuit
![Page 116: Logics of Rational Agencyepacuit/lograt/nasslli2010/lograt-lec5a… · Logics of Rational Agency Lecture 5 Eric Pacuit Tilburg Institute for Logic and Philosophy of Science Tilburg](https://reader035.fdocuments.us/reader035/viewer/2022071410/6105aaf24d2ece0ae545431e/html5/thumbnails/116.jpg)
Conceptual Issue: intentions and beliefs are entangled
1. Intending to act just is a special kind of belief that one will;
Intending to act involves a belief that one will so act;
Intending to act involve a belief that it is possible that onewill so act.
Eric Pacuit
![Page 117: Logics of Rational Agencyepacuit/lograt/nasslli2010/lograt-lec5a… · Logics of Rational Agency Lecture 5 Eric Pacuit Tilburg Institute for Logic and Philosophy of Science Tilburg](https://reader035.fdocuments.us/reader035/viewer/2022071410/6105aaf24d2ece0ae545431e/html5/thumbnails/117.jpg)
Conceptual Issue: intentions and beliefs are entangled
1. Intending to act just is a special kind of belief that one will;
2. Intending to act involves a belief that one will so act;
Intending to act involve a belief that it is possible that onewill so act.
Eric Pacuit
![Page 118: Logics of Rational Agencyepacuit/lograt/nasslli2010/lograt-lec5a… · Logics of Rational Agency Lecture 5 Eric Pacuit Tilburg Institute for Logic and Philosophy of Science Tilburg](https://reader035.fdocuments.us/reader035/viewer/2022071410/6105aaf24d2ece0ae545431e/html5/thumbnails/118.jpg)
Conceptual Issue: intentions and beliefs are entangled
1. Intending to act just is a special kind of belief that one will;
2. Intending to act involves a belief that one will so act;
3. Intending to act involves a belief that it is possible that onewill so act.
Eric Pacuit
![Page 119: Logics of Rational Agencyepacuit/lograt/nasslli2010/lograt-lec5a… · Logics of Rational Agency Lecture 5 Eric Pacuit Tilburg Institute for Logic and Philosophy of Science Tilburg](https://reader035.fdocuments.us/reader035/viewer/2022071410/6105aaf24d2ece0ae545431e/html5/thumbnails/119.jpg)
Conceptual Issue: intentions and beliefs are entangled
1. Intending to act just is a special kind of belief that one will;
2. Intending to act involves a belief that one will so act;
3. Intending to act involves a belief that it is possible that onewill so act.
Eric Pacuit
![Page 120: Logics of Rational Agencyepacuit/lograt/nasslli2010/lograt-lec5a… · Logics of Rational Agency Lecture 5 Eric Pacuit Tilburg Institute for Logic and Philosophy of Science Tilburg](https://reader035.fdocuments.us/reader035/viewer/2022071410/6105aaf24d2ece0ae545431e/html5/thumbnails/120.jpg)
Conceptual Issue: rationality constraints on intentions
1. Consistency: “one’s intentions, taken together with one’sbeliefs fit together into a consistent model of one’s future”
2. Means-ends consistency: “it is irrational that one intends E ,believes that E requires that one intend means M and yet notintend M”
3. Agglomeration: “Intending A and Intending B impliesIntending (A and B)”
M. Bratman. Intention, Belief, Practical, Theoretical. in Spheres of Reason(2009).
Eric Pacuit
![Page 121: Logics of Rational Agencyepacuit/lograt/nasslli2010/lograt-lec5a… · Logics of Rational Agency Lecture 5 Eric Pacuit Tilburg Institute for Logic and Philosophy of Science Tilburg](https://reader035.fdocuments.us/reader035/viewer/2022071410/6105aaf24d2ece0ae545431e/html5/thumbnails/121.jpg)
Conceptual Issue: rationality constraints on intentions
1. Consistency: “one’s intentions, taken together with one’sbeliefs fit together into a consistent model of one’s future”
2. Means-ends consistency: “it is irrational that one intends E ,believes that E requires that one intend means M and yet notintend M”
3. Agglomeration: “Intending A and Intending B impliesIntending (A and B)”
M. Bratman. Intention, Belief, Practical, Theoretical. in Spheres of Reason(2009).
Eric Pacuit
![Page 122: Logics of Rational Agencyepacuit/lograt/nasslli2010/lograt-lec5a… · Logics of Rational Agency Lecture 5 Eric Pacuit Tilburg Institute for Logic and Philosophy of Science Tilburg](https://reader035.fdocuments.us/reader035/viewer/2022071410/6105aaf24d2ece0ae545431e/html5/thumbnails/122.jpg)
Conceptual Issue: rationality constraints on intentions
1. Consistency: “one’s intentions, taken together with one’sbeliefs fit together into a consistent model of one’s future”
2. Means-ends consistency: “it is irrational that one intends E ,believes that E requires that one intend means M and yet notintend M”
3. Agglomeration: “Intending A and Intending B impliesIntending (A and B)”
M. Bratman. Intention, Belief, Practical, Theoretical. in Spheres of Reason(2009).
Eric Pacuit
![Page 123: Logics of Rational Agencyepacuit/lograt/nasslli2010/lograt-lec5a… · Logics of Rational Agency Lecture 5 Eric Pacuit Tilburg Institute for Logic and Philosophy of Science Tilburg](https://reader035.fdocuments.us/reader035/viewer/2022071410/6105aaf24d2ece0ae545431e/html5/thumbnails/123.jpg)
Conceptual Issue: rationality constraints on intentions
1. Consistency: “one’s intentions, taken together with one’sbeliefs fit together into a consistent model of one’s future”
2. Means-ends consistency: “it is irrational that one intends E ,believes that E requires that one intend means M and yet notintend M”
3. Agglomeration: “Intending A and Intending B impliesIntending (A and B)”
M. Bratman. Intention, Belief, Practical, Theoretical. in Spheres of Reason(2009).
Eric Pacuit
![Page 124: Logics of Rational Agencyepacuit/lograt/nasslli2010/lograt-lec5a… · Logics of Rational Agency Lecture 5 Eric Pacuit Tilburg Institute for Logic and Philosophy of Science Tilburg](https://reader035.fdocuments.us/reader035/viewer/2022071410/6105aaf24d2ece0ae545431e/html5/thumbnails/124.jpg)
Intention Dynamics
1. Intentional Action Execution: precise characterizationunder which an agent’s intention transforms into an action.(trying, attempting)
2. Intention Generation: model appropriate principles ofintention generation (practical or instrumental reasoning)
3. Intention Persistence: intentions normally resistreconsideration (bounded agents)
E. Lorini and A. Herzig. A logic of intention and attempt. Synthese 163, pp. 45- 77 (2008).
Eric Pacuit
![Page 125: Logics of Rational Agencyepacuit/lograt/nasslli2010/lograt-lec5a… · Logics of Rational Agency Lecture 5 Eric Pacuit Tilburg Institute for Logic and Philosophy of Science Tilburg](https://reader035.fdocuments.us/reader035/viewer/2022071410/6105aaf24d2ece0ae545431e/html5/thumbnails/125.jpg)
Intention Dynamics
1. Intentional Action Execution: precise characterizationunder which an agent’s intention transforms into an action.(trying, attempting)
2. Intention Generation: model appropriate principles ofintention generation (practical or instrumental reasoning)
3. Intention Persistence: intentions normally resistreconsideration (bounded agents)
E. Lorini and A. Herzig. A logic of intention and attempt. Synthese 163, pp. 45- 77 (2008).
Eric Pacuit
![Page 126: Logics of Rational Agencyepacuit/lograt/nasslli2010/lograt-lec5a… · Logics of Rational Agency Lecture 5 Eric Pacuit Tilburg Institute for Logic and Philosophy of Science Tilburg](https://reader035.fdocuments.us/reader035/viewer/2022071410/6105aaf24d2ece0ae545431e/html5/thumbnails/126.jpg)
Intention Dynamics
1. Intentional Action Execution: precise characterizationunder which an agent’s intention transforms into an action.(trying, attempting)
2. Intention Generation: model appropriate principles ofintention generation (practical or instrumental reasoning)
3. Intention Persistence: intentions normally resistreconsideration (bounded agents)
E. Lorini and A. Herzig. A logic of intention and attempt. Synthese 163, pp. 45- 77 (2008).
Eric Pacuit
![Page 127: Logics of Rational Agencyepacuit/lograt/nasslli2010/lograt-lec5a… · Logics of Rational Agency Lecture 5 Eric Pacuit Tilburg Institute for Logic and Philosophy of Science Tilburg](https://reader035.fdocuments.us/reader035/viewer/2022071410/6105aaf24d2ece0ae545431e/html5/thumbnails/127.jpg)
Intention Dynamics
1. Intentional Action Execution: precise characterizationunder which an agent’s intention transforms into an action.(trying, attempting)
2. Intention Generation: model appropriate principles ofintention generation (practical or instrumental reasoning)
3. Intention Persistence: intentions normally resistreconsideration (bounded agents)
E. Lorini and A. Herzig. A logic of intention and attempt. Synthese 163, pp. 45- 77 (2008).
Eric Pacuit
![Page 128: Logics of Rational Agencyepacuit/lograt/nasslli2010/lograt-lec5a… · Logics of Rational Agency Lecture 5 Eric Pacuit Tilburg Institute for Logic and Philosophy of Science Tilburg](https://reader035.fdocuments.us/reader035/viewer/2022071410/6105aaf24d2ece0ae545431e/html5/thumbnails/128.jpg)
Intention Dynamics
1. Intentional Action Execution: precise characterizationunder which an agent’s intention transforms into an action.(trying, attempting)
2. Intention Generation: model appropriate principles ofintention generation (practical or instrumental reasoning)
3. Intention Persistence: intentions normally resistreconsideration (bounded agents)
E. Lorini and A. Herzig. A logic of intention and attempt. Synthese 163, pp. 45- 77 (2008).
Eric Pacuit
![Page 129: Logics of Rational Agencyepacuit/lograt/nasslli2010/lograt-lec5a… · Logics of Rational Agency Lecture 5 Eric Pacuit Tilburg Institute for Logic and Philosophy of Science Tilburg](https://reader035.fdocuments.us/reader035/viewer/2022071410/6105aaf24d2ece0ae545431e/html5/thumbnails/129.jpg)
Belief and Intention Revision
1. Strong analogy between the problem of plan/intention changeand belief change. When an agent learns that his plans are nolonger viable, he must change them so that they account forthe new information.
2. There are important differences between the two problems: Ifthe agent has committed to doing action a at time i (perhapson condition ϕ), there is always a specific reason for thiscommitment. In contrast, standard models of belief change donot record specific reasons for each belief.
3. Finally, the two problems are intertwined: This is because wemust not only maintain that the agent’s beliefs and plans areindividually consistent, but also that they are jointly coherent.
Eric Pacuit
![Page 130: Logics of Rational Agencyepacuit/lograt/nasslli2010/lograt-lec5a… · Logics of Rational Agency Lecture 5 Eric Pacuit Tilburg Institute for Logic and Philosophy of Science Tilburg](https://reader035.fdocuments.us/reader035/viewer/2022071410/6105aaf24d2ece0ae545431e/html5/thumbnails/130.jpg)
Belief and Intention Revision
1. Strong analogy between the problem of plan/intention changeand belief change.
When an agent learns that his plans are nolonger viable, he must change them so that they account forthe new information.
2. There are important differences between the two problems: Ifthe agent has committed to doing action a at time i (perhapson condition ϕ), there is always a specific reason for thiscommitment. In contrast, standard models of belief change donot record specific reasons for each belief.
3. Finally, the two problems are intertwined: This is because wemust not only maintain that the agent’s beliefs and plans areindividually consistent, but also that they are jointly coherent.
Eric Pacuit
![Page 131: Logics of Rational Agencyepacuit/lograt/nasslli2010/lograt-lec5a… · Logics of Rational Agency Lecture 5 Eric Pacuit Tilburg Institute for Logic and Philosophy of Science Tilburg](https://reader035.fdocuments.us/reader035/viewer/2022071410/6105aaf24d2ece0ae545431e/html5/thumbnails/131.jpg)
Belief and Intention Revision
1. Strong analogy between the problem of plan/intention changeand belief change. When an agent learns that his plans are nolonger viable, he must change them so that they account forthe new information.
2. There are important differences between the two problems: Ifthe agent has committed to doing action a at time i (perhapson condition ϕ), there is always a specific reason for thiscommitment. In contrast, standard models of belief change donot record specific reasons for each belief.
3. Finally, the two problems are intertwined: This is because wemust not only maintain that the agent’s beliefs and plans areindividually consistent, but also that they are jointly coherent.
Eric Pacuit
![Page 132: Logics of Rational Agencyepacuit/lograt/nasslli2010/lograt-lec5a… · Logics of Rational Agency Lecture 5 Eric Pacuit Tilburg Institute for Logic and Philosophy of Science Tilburg](https://reader035.fdocuments.us/reader035/viewer/2022071410/6105aaf24d2ece0ae545431e/html5/thumbnails/132.jpg)
Belief and Intention Revision
1. Strong analogy between the problem of plan/intention changeand belief change. When an agent learns that his plans are nolonger viable, he must change them so that they account forthe new information.
2. There are important differences between the two problems:
Ifthe agent has committed to doing action a at time i (perhapson condition ϕ), there is always a specific reason for thiscommitment. In contrast, standard models of belief change donot record specific reasons for each belief.
3. Finally, the two problems are intertwined: This is because wemust not only maintain that the agent’s beliefs and plans areindividually consistent, but also that they are jointly coherent.
Eric Pacuit
![Page 133: Logics of Rational Agencyepacuit/lograt/nasslli2010/lograt-lec5a… · Logics of Rational Agency Lecture 5 Eric Pacuit Tilburg Institute for Logic and Philosophy of Science Tilburg](https://reader035.fdocuments.us/reader035/viewer/2022071410/6105aaf24d2ece0ae545431e/html5/thumbnails/133.jpg)
Belief and Intention Revision
1. Strong analogy between the problem of plan/intention changeand belief change. When an agent learns that his plans are nolonger viable, he must change them so that they account forthe new information.
2. There are important differences between the two problems: Ifthe agent has committed to doing action a at time i (perhapson condition ϕ), there is always a specific reason for thiscommitment. In contrast, standard models of belief change donot record specific reasons for each belief.
3. Finally, the two problems are intertwined: This is because wemust not only maintain that the agent’s beliefs and plans areindividually consistent, but also that they are jointly coherent.
Eric Pacuit
![Page 134: Logics of Rational Agencyepacuit/lograt/nasslli2010/lograt-lec5a… · Logics of Rational Agency Lecture 5 Eric Pacuit Tilburg Institute for Logic and Philosophy of Science Tilburg](https://reader035.fdocuments.us/reader035/viewer/2022071410/6105aaf24d2ece0ae545431e/html5/thumbnails/134.jpg)
Belief and Intention Revision
1. Strong analogy between the problem of plan/intention changeand belief change. When an agent learns that his plans are nolonger viable, he must change them so that they account forthe new information.
2. There are important differences between the two problems: Ifthe agent has committed to doing action a at time i (perhapson condition ϕ), there is always a specific reason for thiscommitment. In contrast, standard models of belief change donot record specific reasons for each belief.
3. Finally, the two problems are intertwined:
This is because wemust not only maintain that the agent’s beliefs and plans areindividually consistent, but also that they are jointly coherent.
Eric Pacuit
![Page 135: Logics of Rational Agencyepacuit/lograt/nasslli2010/lograt-lec5a… · Logics of Rational Agency Lecture 5 Eric Pacuit Tilburg Institute for Logic and Philosophy of Science Tilburg](https://reader035.fdocuments.us/reader035/viewer/2022071410/6105aaf24d2ece0ae545431e/html5/thumbnails/135.jpg)
Belief and Intention Revision
1. Strong analogy between the problem of plan/intention changeand belief change. When an agent learns that his plans are nolonger viable, he must change them so that they account forthe new information.
2. There are important differences between the two problems: Ifthe agent has committed to doing action a at time i (perhapson condition ϕ), there is always a specific reason for thiscommitment. In contrast, standard models of belief change donot record specific reasons for each belief.
3. Finally, the two problems are intertwined: This is because wemust not only maintain that the agent’s beliefs and plans areindividually consistent, but also that they are jointly coherent.
Eric Pacuit
![Page 136: Logics of Rational Agencyepacuit/lograt/nasslli2010/lograt-lec5a… · Logics of Rational Agency Lecture 5 Eric Pacuit Tilburg Institute for Logic and Philosophy of Science Tilburg](https://reader035.fdocuments.us/reader035/viewer/2022071410/6105aaf24d2ece0ae545431e/html5/thumbnails/136.jpg)
Belief and Intention Revision
1. How should we describe the “mental state”?Propositional formulas
2. What is a coherent description?A belief state is a consistent and deductively closed set ofpropositional formulas
3. What are the inputs?Consistent propositional formula
4. How should we characterize the revision operator?AGM postulates, Dynamic Doxastic Logic
Eric Pacuit
![Page 137: Logics of Rational Agencyepacuit/lograt/nasslli2010/lograt-lec5a… · Logics of Rational Agency Lecture 5 Eric Pacuit Tilburg Institute for Logic and Philosophy of Science Tilburg](https://reader035.fdocuments.us/reader035/viewer/2022071410/6105aaf24d2ece0ae545431e/html5/thumbnails/137.jpg)
Belief and Intention Revision
1. How should we describe the “mental state”?Propositional formulas
2. What is a coherent description?A belief state is a consistent and deductively closed set ofpropositional formulas
3. What are the inputs?Consistent propositional formula
4. How should we characterize the revision operator?AGM postulates, Dynamic Doxastic Logic
Eric Pacuit
![Page 138: Logics of Rational Agencyepacuit/lograt/nasslli2010/lograt-lec5a… · Logics of Rational Agency Lecture 5 Eric Pacuit Tilburg Institute for Logic and Philosophy of Science Tilburg](https://reader035.fdocuments.us/reader035/viewer/2022071410/6105aaf24d2ece0ae545431e/html5/thumbnails/138.jpg)
Goal: Find a logic where consistency represents
1. the agent’s beliefs are consistent,
2. the agent’s future plans are consistent and
3. the beliefs and intentions together form a coherent picture ofwhat may happen (and how the agent’s own actions will playa role in what may happen).
Eric Pacuit
![Page 139: Logics of Rational Agencyepacuit/lograt/nasslli2010/lograt-lec5a… · Logics of Rational Agency Lecture 5 Eric Pacuit Tilburg Institute for Logic and Philosophy of Science Tilburg](https://reader035.fdocuments.us/reader035/viewer/2022071410/6105aaf24d2ece0ae545431e/html5/thumbnails/139.jpg)
Goal: Find a logic where consistency represents
1. the agent’s beliefs are consistent,
2. the agent’s future plans are consistent and
3. the beliefs and intentions together form a coherent picture ofwhat may happen (and how the agent’s own actions will playa role in what may happen).
Eric Pacuit
![Page 140: Logics of Rational Agencyepacuit/lograt/nasslli2010/lograt-lec5a… · Logics of Rational Agency Lecture 5 Eric Pacuit Tilburg Institute for Logic and Philosophy of Science Tilburg](https://reader035.fdocuments.us/reader035/viewer/2022071410/6105aaf24d2ece0ae545431e/html5/thumbnails/140.jpg)
Goal: Find a logic where consistency represents
1. the agent’s beliefs are consistent,
2. the agent’s future plans are consistent and
3. the beliefs and intentions together form a coherent picture ofwhat may happen (and how the agent’s own actions will playa role in what may happen).
Eric Pacuit
![Page 141: Logics of Rational Agencyepacuit/lograt/nasslli2010/lograt-lec5a… · Logics of Rational Agency Lecture 5 Eric Pacuit Tilburg Institute for Logic and Philosophy of Science Tilburg](https://reader035.fdocuments.us/reader035/viewer/2022071410/6105aaf24d2ece0ae545431e/html5/thumbnails/141.jpg)
Goal: Find a logic where consistency represents
1. the agent’s beliefs are consistent,
2. the agent’s future plans are consistent and
3. the beliefs and intentions together form a coherent picture ofwhat may happen (and how the agent’s own actions will playa role in what may happen).
Eric Pacuit
![Page 142: Logics of Rational Agencyepacuit/lograt/nasslli2010/lograt-lec5a… · Logics of Rational Agency Lecture 5 Eric Pacuit Tilburg Institute for Logic and Philosophy of Science Tilburg](https://reader035.fdocuments.us/reader035/viewer/2022071410/6105aaf24d2ece0ae545431e/html5/thumbnails/142.jpg)
Background: BDI Logics
Stemming from Bratman’s planning theory of intention a numberof logics of rational agency have been developed:
I Cohen and Levesque Example ; Rao and Georgeff (BDI); Meyerand van der Hoek (KARO); and many others.
Some common features
I Underlying temporal model
I Belief, Desire, Intention, Plans, Actions are defined withcorresponding operators in a language
J.-J. Meyer and F. Veltman. Intelligent Agents and Common Sense Reasoning.Handbook of Modal Logic, 2007.
Eric Pacuit
![Page 143: Logics of Rational Agencyepacuit/lograt/nasslli2010/lograt-lec5a… · Logics of Rational Agency Lecture 5 Eric Pacuit Tilburg Institute for Logic and Philosophy of Science Tilburg](https://reader035.fdocuments.us/reader035/viewer/2022071410/6105aaf24d2ece0ae545431e/html5/thumbnails/143.jpg)
Background: BDI Logics
Stemming from Bratman’s planning theory of intention a numberof logics of rational agency have been developed:
I Cohen and Levesque Example ; Rao and Georgeff (BDI); Meyerand van der Hoek (KARO); and many others.
Some common features
I Underlying temporal model
I Belief, Desire, Intention, Plans, Actions are defined withcorresponding operators in a language
J.-J. Meyer and F. Veltman. Intelligent Agents and Common Sense Reasoning.Handbook of Modal Logic, 2007.
Eric Pacuit
![Page 144: Logics of Rational Agencyepacuit/lograt/nasslli2010/lograt-lec5a… · Logics of Rational Agency Lecture 5 Eric Pacuit Tilburg Institute for Logic and Philosophy of Science Tilburg](https://reader035.fdocuments.us/reader035/viewer/2022071410/6105aaf24d2ece0ae545431e/html5/thumbnails/144.jpg)
A Methodological Issue
What are we formalizing? How will the logical framework be used?
Two Extremes:
1. Formalizing a (philosophical) theory of rational agency:philosophers as intuition pumps generating “problems” for thelogical frameworks (eg., the “side-effect problem”).
2. Reasoning about multiagent systems: Three main applicationsof BDI logics: 1. a specification language for a MAS, 2. aprogramming language, and 3. verification language.
W. van der Hoek and M. Wooldridge. Towards a logic of rational agency. LogicJournal of the IGPL 11 (2), 2003.
Eric Pacuit
![Page 145: Logics of Rational Agencyepacuit/lograt/nasslli2010/lograt-lec5a… · Logics of Rational Agency Lecture 5 Eric Pacuit Tilburg Institute for Logic and Philosophy of Science Tilburg](https://reader035.fdocuments.us/reader035/viewer/2022071410/6105aaf24d2ece0ae545431e/html5/thumbnails/145.jpg)
A Methodological Issue
What are we formalizing? How will the logical framework be used?
Two Extremes:
1. Formalizing a (philosophical) theory of rational agency:
philosophers as intuition pumps generating “problems” for thelogical frameworks (eg., the “side-effect problem”).
2. Reasoning about multiagent systems: Three main applicationsof BDI logics: 1. a specification language for a MAS, 2. aprogramming language, and 3. verification language.
W. van der Hoek and M. Wooldridge. Towards a logic of rational agency. LogicJournal of the IGPL 11 (2), 2003.
Eric Pacuit
![Page 146: Logics of Rational Agencyepacuit/lograt/nasslli2010/lograt-lec5a… · Logics of Rational Agency Lecture 5 Eric Pacuit Tilburg Institute for Logic and Philosophy of Science Tilburg](https://reader035.fdocuments.us/reader035/viewer/2022071410/6105aaf24d2ece0ae545431e/html5/thumbnails/146.jpg)
A Methodological Issue
What are we formalizing? How will the logical framework be used?
Two Extremes:
1. Formalizing a (philosophical) theory of rational agency:philosophers as intuition pumps generating “problems” for thelogical frameworks (eg., the “side-effect problem”).
2. Reasoning about multiagent systems: Three main applicationsof BDI logics: 1. a specification language for a MAS, 2. aprogramming language, and 3. verification language.
W. van der Hoek and M. Wooldridge. Towards a logic of rational agency. LogicJournal of the IGPL 11 (2), 2003.
Eric Pacuit
![Page 147: Logics of Rational Agencyepacuit/lograt/nasslli2010/lograt-lec5a… · Logics of Rational Agency Lecture 5 Eric Pacuit Tilburg Institute for Logic and Philosophy of Science Tilburg](https://reader035.fdocuments.us/reader035/viewer/2022071410/6105aaf24d2ece0ae545431e/html5/thumbnails/147.jpg)
A Methodological Issue
What are we formalizing? How will the logical framework be used?
Two Extremes:
1. Formalizing a (philosophical) theory of rational agency:philosophers as intuition pumps generating “problems” for thelogical frameworks (eg., the “side-effect problem”).
2. Reasoning about multiagent systems:
Three main applicationsof BDI logics: 1. a specification language for a MAS, 2. aprogramming language, and 3. verification language.
W. van der Hoek and M. Wooldridge. Towards a logic of rational agency. LogicJournal of the IGPL 11 (2), 2003.
Eric Pacuit
![Page 148: Logics of Rational Agencyepacuit/lograt/nasslli2010/lograt-lec5a… · Logics of Rational Agency Lecture 5 Eric Pacuit Tilburg Institute for Logic and Philosophy of Science Tilburg](https://reader035.fdocuments.us/reader035/viewer/2022071410/6105aaf24d2ece0ae545431e/html5/thumbnails/148.jpg)
A Methodological Issue
What are we formalizing? How will the logical framework be used?
Two Extremes:
1. Formalizing a (philosophical) theory of rational agency:philosophers as intuition pumps generating “problems” for thelogical frameworks (eg., the “side-effect problem”).
2. Reasoning about multiagent systems: Three main applicationsof BDI logics: 1. a specification language for a MAS, 2. aprogramming language, and 3. verification language.
W. van der Hoek and M. Wooldridge. Towards a logic of rational agency. LogicJournal of the IGPL 11 (2), 2003.
Eric Pacuit
![Page 149: Logics of Rational Agencyepacuit/lograt/nasslli2010/lograt-lec5a… · Logics of Rational Agency Lecture 5 Eric Pacuit Tilburg Institute for Logic and Philosophy of Science Tilburg](https://reader035.fdocuments.us/reader035/viewer/2022071410/6105aaf24d2ece0ae545431e/html5/thumbnails/149.jpg)
Describing the Mental StateW. van der Hoek, W. Jamroga and M. Wooldridge. Towards a theory of intentionrevision. Synthese 155, pgs. 265 - 290 (2007).
Γ = 〈B,D, 〈I,A〉,¶〉
1. B: beliefs
2. D: desires
3. 〈I,A〉: intentions and active plans
4. ¶: practical reasoning rules (“know how”)
Eric Pacuit
![Page 150: Logics of Rational Agencyepacuit/lograt/nasslli2010/lograt-lec5a… · Logics of Rational Agency Lecture 5 Eric Pacuit Tilburg Institute for Logic and Philosophy of Science Tilburg](https://reader035.fdocuments.us/reader035/viewer/2022071410/6105aaf24d2ece0ae545431e/html5/thumbnails/150.jpg)
Describing the Mental StateW. van der Hoek, W. Jamroga and M. Wooldridge. Towards a theory of intentionrevision. Synthese 155, pgs. 265 - 290 (2007).
Γ = 〈B,D, 〈I,A〉,¶〉
1. B: beliefs
2. D: desires
3. 〈I,A〉: intentions and active plans
4. ¶: practical reasoning rules (“know how”)
Eric Pacuit
![Page 151: Logics of Rational Agencyepacuit/lograt/nasslli2010/lograt-lec5a… · Logics of Rational Agency Lecture 5 Eric Pacuit Tilburg Institute for Logic and Philosophy of Science Tilburg](https://reader035.fdocuments.us/reader035/viewer/2022071410/6105aaf24d2ece0ae545431e/html5/thumbnails/151.jpg)
Describing the Mental StateW. van der Hoek, W. Jamroga and M. Wooldridge. Towards a theory of intentionrevision. Synthese 155, pgs. 265 - 290 (2007).
Γ = 〈B,D, 〈I,A〉,¶〉
1. B: beliefs
2. D: desires
3. 〈I,A〉: intentions and active plans
4. ¶: practical reasoning rules (“know how”)
Eric Pacuit
![Page 152: Logics of Rational Agencyepacuit/lograt/nasslli2010/lograt-lec5a… · Logics of Rational Agency Lecture 5 Eric Pacuit Tilburg Institute for Logic and Philosophy of Science Tilburg](https://reader035.fdocuments.us/reader035/viewer/2022071410/6105aaf24d2ece0ae545431e/html5/thumbnails/152.jpg)
Describing the Mental StateW. van der Hoek, W. Jamroga and M. Wooldridge. Towards a theory of intentionrevision. Synthese 155, pgs. 265 - 290 (2007).
Γ = 〈B,D, 〈I,A〉,¶〉
1. B: beliefs
2. D: desires
3. 〈I,A〉: intentions and active plans
4. ¶: practical reasoning rules (“know how”)
Eric Pacuit
![Page 153: Logics of Rational Agencyepacuit/lograt/nasslli2010/lograt-lec5a… · Logics of Rational Agency Lecture 5 Eric Pacuit Tilburg Institute for Logic and Philosophy of Science Tilburg](https://reader035.fdocuments.us/reader035/viewer/2022071410/6105aaf24d2ece0ae545431e/html5/thumbnails/153.jpg)
Describing the Mental StateW. van der Hoek, W. Jamroga and M. Wooldridge. Towards a theory of intentionrevision. Synthese 155, pgs. 265 - 290 (2007).
Γ = 〈B,D, 〈I,A〉,¶〉
1. B: beliefs
2. D: desires
3. 〈I,A〉: intentions and active plans
4. ¶: practical reasoning rules (“know how”)
Eric Pacuit
![Page 154: Logics of Rational Agencyepacuit/lograt/nasslli2010/lograt-lec5a… · Logics of Rational Agency Lecture 5 Eric Pacuit Tilburg Institute for Logic and Philosophy of Science Tilburg](https://reader035.fdocuments.us/reader035/viewer/2022071410/6105aaf24d2ece0ae545431e/html5/thumbnails/154.jpg)
Describing the Mental StateW. van der Hoek, W. Jamroga and M. Wooldridge. Towards a theory of intentionrevision. Synthese 155, pgs. 265 - 290 (2007).
Γ = 〈B,D, 〈I,A〉,P〉
I Beliefs are sets of Linear Temporal Logic formulas (eg., ©ϕ)
I Desires are (possibly inconsistent) sets of Linear TemporalLogic formulas
I Practical reasoning rules: α← α1, α2, . . . , αn (“if Tα is anintention then T (α1 ∧ · · · ∧ αn) is a possible fulfillment...”)
I Intentions are derived from the agents current active plans(trees of practical reasoning rules)
Eric Pacuit
![Page 155: Logics of Rational Agencyepacuit/lograt/nasslli2010/lograt-lec5a… · Logics of Rational Agency Lecture 5 Eric Pacuit Tilburg Institute for Logic and Philosophy of Science Tilburg](https://reader035.fdocuments.us/reader035/viewer/2022071410/6105aaf24d2ece0ae545431e/html5/thumbnails/155.jpg)
Describing the Mental StateW. van der Hoek, W. Jamroga and M. Wooldridge. Towards a theory of intentionrevision. Synthese 155, pgs. 265 - 290 (2007).
Γ = 〈B,D, 〈I,A〉,P〉
I Beliefs are sets of Linear Temporal Logic formulas (eg., ©ϕ)
I Desires are (possibly inconsistent) sets of Linear TemporalLogic formulas
I Practical reasoning rules: α← α1, α2, . . . , αn (“if Tα is anintention then T (α1 ∧ · · · ∧ αn) is a possible fulfillment...”)
I Intentions are derived from the agents current active plans(trees of practical reasoning rules)
Eric Pacuit
![Page 156: Logics of Rational Agencyepacuit/lograt/nasslli2010/lograt-lec5a… · Logics of Rational Agency Lecture 5 Eric Pacuit Tilburg Institute for Logic and Philosophy of Science Tilburg](https://reader035.fdocuments.us/reader035/viewer/2022071410/6105aaf24d2ece0ae545431e/html5/thumbnails/156.jpg)
Describing the Mental StateW. van der Hoek, W. Jamroga and M. Wooldridge. Towards a theory of intentionrevision. Synthese 155, pgs. 265 - 290 (2007).
Γ = 〈B,D, 〈I,A〉,P〉
I Beliefs are sets of Linear Temporal Logic formulas (eg., ©ϕ)
I Desires are (possibly inconsistent) sets of Linear TemporalLogic formulas
I Practical reasoning rules: α← α1, α2, . . . , αn (“if Tα is anintention then T (α1 ∧ · · · ∧ αn) is a possible fulfillment...”)
I Intentions are derived from the agents current active plans(trees of practical reasoning rules)
Eric Pacuit
![Page 157: Logics of Rational Agencyepacuit/lograt/nasslli2010/lograt-lec5a… · Logics of Rational Agency Lecture 5 Eric Pacuit Tilburg Institute for Logic and Philosophy of Science Tilburg](https://reader035.fdocuments.us/reader035/viewer/2022071410/6105aaf24d2ece0ae545431e/html5/thumbnails/157.jpg)
Describing the Mental StateW. van der Hoek, W. Jamroga and M. Wooldridge. Towards a theory of intentionrevision. Synthese 155, pgs. 265 - 290 (2007).
Γ = 〈B,D, 〈I,A〉,P〉
I Beliefs are sets of Linear Temporal Logic formulas (eg., ©ϕ)
I Desires are (possibly inconsistent) sets of Linear TemporalLogic formulas
I Practical reasoning rules: α← α1, α2, . . . , αn (“if Tα is anintention then T (α1 ∧ · · · ∧ αn) is a possible fulfillment...”)
I Intentions are derived from the agents current active plans(trees of practical reasoning rules)
Eric Pacuit
![Page 158: Logics of Rational Agencyepacuit/lograt/nasslli2010/lograt-lec5a… · Logics of Rational Agency Lecture 5 Eric Pacuit Tilburg Institute for Logic and Philosophy of Science Tilburg](https://reader035.fdocuments.us/reader035/viewer/2022071410/6105aaf24d2ece0ae545431e/html5/thumbnails/158.jpg)
What is the appropriate underlying logic?
Many proposals, but no clear consensus...
I KD45 for B?
I Bϕ→ Goalϕ?
I Goalϕ→ ¬B¬ϕ?
I Goalϕ→ BGoalϕ?
I Temporal logic, action logic, doxastic logic, combinations,etc., etc.
Eric Pacuit
![Page 159: Logics of Rational Agencyepacuit/lograt/nasslli2010/lograt-lec5a… · Logics of Rational Agency Lecture 5 Eric Pacuit Tilburg Institute for Logic and Philosophy of Science Tilburg](https://reader035.fdocuments.us/reader035/viewer/2022071410/6105aaf24d2ece0ae545431e/html5/thumbnails/159.jpg)
What is the appropriate underlying logic?
Many proposals, but no clear consensus...
I KD45 for B?
I Bϕ→ Goalϕ?
I Goalϕ→ ¬B¬ϕ?
I Goalϕ→ BGoalϕ?
I Temporal logic, action logic, doxastic logic, combinations,etc., etc.
Eric Pacuit
![Page 160: Logics of Rational Agencyepacuit/lograt/nasslli2010/lograt-lec5a… · Logics of Rational Agency Lecture 5 Eric Pacuit Tilburg Institute for Logic and Philosophy of Science Tilburg](https://reader035.fdocuments.us/reader035/viewer/2022071410/6105aaf24d2ece0ae545431e/html5/thumbnails/160.jpg)
What is the appropriate underlying logic?
Many proposals, but no clear consensus...
I KD45 for B?
I Bϕ→ Goalϕ?
I Goalϕ→ ¬B¬ϕ?
I Goalϕ→ BGoalϕ?
I Temporal logic, action logic, doxastic logic, combinations,etc., etc.
Eric Pacuit
![Page 161: Logics of Rational Agencyepacuit/lograt/nasslli2010/lograt-lec5a… · Logics of Rational Agency Lecture 5 Eric Pacuit Tilburg Institute for Logic and Philosophy of Science Tilburg](https://reader035.fdocuments.us/reader035/viewer/2022071410/6105aaf24d2ece0ae545431e/html5/thumbnails/161.jpg)
What is the appropriate underlying logic?
Many proposals, but no clear consensus...
I KD45 for B?
I Bϕ→ Goalϕ?
I Goalϕ→ ¬B¬ϕ?
I Goalϕ→ BGoalϕ?
I Temporal logic, action logic, doxastic logic, combinations,etc., etc.
Eric Pacuit
![Page 162: Logics of Rational Agencyepacuit/lograt/nasslli2010/lograt-lec5a… · Logics of Rational Agency Lecture 5 Eric Pacuit Tilburg Institute for Logic and Philosophy of Science Tilburg](https://reader035.fdocuments.us/reader035/viewer/2022071410/6105aaf24d2ece0ae545431e/html5/thumbnails/162.jpg)
What is the appropriate underlying logic?
Many proposals, but no clear consensus...
I KD45 for B?
I Bϕ→ Goalϕ?
I Goalϕ→ ¬B¬ϕ?
I Goalϕ→ BGoalϕ?
I Temporal logic, action logic, doxastic logic, combinations,etc., etc.
Eric Pacuit
![Page 163: Logics of Rational Agencyepacuit/lograt/nasslli2010/lograt-lec5a… · Logics of Rational Agency Lecture 5 Eric Pacuit Tilburg Institute for Logic and Philosophy of Science Tilburg](https://reader035.fdocuments.us/reader035/viewer/2022071410/6105aaf24d2ece0ae545431e/html5/thumbnails/163.jpg)
What is the appropriate underlying logic?
Many proposals, but no clear consensus...
I KD45 for B?
I Bϕ→ Goalϕ?
I Goalϕ→ ¬B¬ϕ?
I Goalϕ→ BGoalϕ?
I Temporal logic, action logic, doxastic logic, combinations,etc., etc.
Eric Pacuit
![Page 164: Logics of Rational Agencyepacuit/lograt/nasslli2010/lograt-lec5a… · Logics of Rational Agency Lecture 5 Eric Pacuit Tilburg Institute for Logic and Philosophy of Science Tilburg](https://reader035.fdocuments.us/reader035/viewer/2022071410/6105aaf24d2ece0ae545431e/html5/thumbnails/164.jpg)
What is the appropriate underlying logic?
Many proposals, but no clear consensus...
I KD45 for B?
I Bϕ→ Goalϕ?
I Goalϕ→ ¬B¬ϕ?
I Goalϕ→ BGoalϕ?
I Temporal logic, action logic, doxastic logic, combinations,etc., etc.
Eric Pacuit
![Page 165: Logics of Rational Agencyepacuit/lograt/nasslli2010/lograt-lec5a… · Logics of Rational Agency Lecture 5 Eric Pacuit Tilburg Institute for Logic and Philosophy of Science Tilburg](https://reader035.fdocuments.us/reader035/viewer/2022071410/6105aaf24d2ece0ae545431e/html5/thumbnails/165.jpg)
Focusing the Discussion
Start from an explicit description of what is being modeled: eg., a“planner” using a “database” to maintain its current set of beliefsand plans.
Y. Shoham. Logic of Intention and the Database Perspective. JPL 2009.
How should we describe the “mental state”?What type of entries are in the database?
1. Beliefs (about future states, which actions are available pluswhat the agent might do)
2. Current instructions from the planner
Eric Pacuit
![Page 166: Logics of Rational Agencyepacuit/lograt/nasslli2010/lograt-lec5a… · Logics of Rational Agency Lecture 5 Eric Pacuit Tilburg Institute for Logic and Philosophy of Science Tilburg](https://reader035.fdocuments.us/reader035/viewer/2022071410/6105aaf24d2ece0ae545431e/html5/thumbnails/166.jpg)
Focusing the Discussion
Start from an explicit description of what is being modeled: eg., a“planner” using a “database” to maintain its current set of beliefsand plans.
Y. Shoham. Logic of Intention and the Database Perspective. JPL 2009.
How should we describe the “mental state”?What type of entries are in the database?
1. Beliefs (about future states, which actions are available pluswhat the agent might do)
2. Current instructions from the planner
Eric Pacuit
![Page 167: Logics of Rational Agencyepacuit/lograt/nasslli2010/lograt-lec5a… · Logics of Rational Agency Lecture 5 Eric Pacuit Tilburg Institute for Logic and Philosophy of Science Tilburg](https://reader035.fdocuments.us/reader035/viewer/2022071410/6105aaf24d2ece0ae545431e/html5/thumbnails/167.jpg)
Focusing the Discussion
Start from an explicit description of what is being modeled: eg., a“planner” using a “database” to maintain its current set of beliefsand plans.
Y. Shoham. Logic of Intention and the Database Perspective. JPL 2009.
How should we describe the “mental state”?What type of entries are in the database?
1. Beliefs (about future states, which actions are available pluswhat the agent might do)
2. Current instructions from the planner
Eric Pacuit
![Page 168: Logics of Rational Agencyepacuit/lograt/nasslli2010/lograt-lec5a… · Logics of Rational Agency Lecture 5 Eric Pacuit Tilburg Institute for Logic and Philosophy of Science Tilburg](https://reader035.fdocuments.us/reader035/viewer/2022071410/6105aaf24d2ece0ae545431e/html5/thumbnails/168.jpg)
Contingent vs. Non-contingent Beliefs
Post-conditions of intended actions are justifiably believed by themere fact that the agent has committed to bringing them about.
On the other hand, pre-conditions may still pose a practicalproblem yet to be solved.
Eric Pacuit
![Page 169: Logics of Rational Agencyepacuit/lograt/nasslli2010/lograt-lec5a… · Logics of Rational Agency Lecture 5 Eric Pacuit Tilburg Institute for Logic and Philosophy of Science Tilburg](https://reader035.fdocuments.us/reader035/viewer/2022071410/6105aaf24d2ece0ae545431e/html5/thumbnails/169.jpg)
Contingent vs. Non-contingent Beliefs
Post-conditions of intended actions are justifiably believed by themere fact that the agent has committed to bringing them about.
On the other hand, pre-conditions may still pose a practicalproblem yet to be solved.
Eric Pacuit
![Page 170: Logics of Rational Agencyepacuit/lograt/nasslli2010/lograt-lec5a… · Logics of Rational Agency Lecture 5 Eric Pacuit Tilburg Institute for Logic and Philosophy of Science Tilburg](https://reader035.fdocuments.us/reader035/viewer/2022071410/6105aaf24d2ece0ae545431e/html5/thumbnails/170.jpg)
Contingent vs. Non-contingent Beliefs
“My belief that I will be at Tanner Library this afternoon is basedon my knowledge that I intend to go there.
If I reconsider thisintention, I must bracket the support it provides for this belief andothers. I must take care not to keep assuming I will be at Tanner,even while reconsidering my intention to go there....Keeping trackof the ways in which one’s beliefs depend on intentions beingreconsidered may become a fairly complex matter, especially asone reconsiders more extensive elements in one’s prior plans. Butthis should not be taken to show that one may rationally proceedwithout adjusting one’s beliefs as one reconsiders. Rather, it showsjust how complicated — and so, costly — reconsideration of priorintentions can be.”
[Bratman, pg. 63, my emphasis]
Eric Pacuit
![Page 171: Logics of Rational Agencyepacuit/lograt/nasslli2010/lograt-lec5a… · Logics of Rational Agency Lecture 5 Eric Pacuit Tilburg Institute for Logic and Philosophy of Science Tilburg](https://reader035.fdocuments.us/reader035/viewer/2022071410/6105aaf24d2ece0ae545431e/html5/thumbnails/171.jpg)
Contingent vs. Non-contingent Beliefs
“My belief that I will be at Tanner Library this afternoon is basedon my knowledge that I intend to go there. If I reconsider thisintention, I must bracket the support it provides for this belief andothers. I must take care not to keep assuming I will be at Tanner,even while reconsidering my intention to go there....
Keeping trackof the ways in which one’s beliefs depend on intentions beingreconsidered may become a fairly complex matter, especially asone reconsiders more extensive elements in one’s prior plans. Butthis should not be taken to show that one may rationally proceedwithout adjusting one’s beliefs as one reconsiders. Rather, it showsjust how complicated — and so, costly — reconsideration of priorintentions can be.”
[Bratman, pg. 63, my emphasis]
Eric Pacuit
![Page 172: Logics of Rational Agencyepacuit/lograt/nasslli2010/lograt-lec5a… · Logics of Rational Agency Lecture 5 Eric Pacuit Tilburg Institute for Logic and Philosophy of Science Tilburg](https://reader035.fdocuments.us/reader035/viewer/2022071410/6105aaf24d2ece0ae545431e/html5/thumbnails/172.jpg)
Contingent vs. Non-contingent Beliefs
“My belief that I will be at Tanner Library this afternoon is basedon my knowledge that I intend to go there. If I reconsider thisintention, I must bracket the support it provides for this belief andothers. I must take care not to keep assuming I will be at Tanner,even while reconsidering my intention to go there....Keeping trackof the ways in which one’s beliefs depend on intentions beingreconsidered may become a fairly complex matter, especially asone reconsiders more extensive elements in one’s prior plans.
Butthis should not be taken to show that one may rationally proceedwithout adjusting one’s beliefs as one reconsiders. Rather, it showsjust how complicated — and so, costly — reconsideration of priorintentions can be.”
[Bratman, pg. 63, my emphasis]
Eric Pacuit
![Page 173: Logics of Rational Agencyepacuit/lograt/nasslli2010/lograt-lec5a… · Logics of Rational Agency Lecture 5 Eric Pacuit Tilburg Institute for Logic and Philosophy of Science Tilburg](https://reader035.fdocuments.us/reader035/viewer/2022071410/6105aaf24d2ece0ae545431e/html5/thumbnails/173.jpg)
Contingent vs. Non-contingent Beliefs
“My belief that I will be at Tanner Library this afternoon is basedon my knowledge that I intend to go there. If I reconsider thisintention, I must bracket the support it provides for this belief andothers. I must take care not to keep assuming I will be at Tanner,even while reconsidering my intention to go there....Keeping trackof the ways in which one’s beliefs depend on intentions beingreconsidered may become a fairly complex matter, especially asone reconsiders more extensive elements in one’s prior plans. Butthis should not be taken to show that one may rationally proceedwithout adjusting one’s beliefs as one reconsiders.
Rather, it showsjust how complicated — and so, costly — reconsideration of priorintentions can be.”
[Bratman, pg. 63, my emphasis]
Eric Pacuit
![Page 174: Logics of Rational Agencyepacuit/lograt/nasslli2010/lograt-lec5a… · Logics of Rational Agency Lecture 5 Eric Pacuit Tilburg Institute for Logic and Philosophy of Science Tilburg](https://reader035.fdocuments.us/reader035/viewer/2022071410/6105aaf24d2ece0ae545431e/html5/thumbnails/174.jpg)
Contingent vs. Non-contingent Beliefs
“My belief that I will be at Tanner Library this afternoon is basedon my knowledge that I intend to go there. If I reconsider thisintention, I must bracket the support it provides for this belief andothers. I must take care not to keep assuming I will be at Tanner,even while reconsidering my intention to go there....Keeping trackof the ways in which one’s beliefs depend on intentions beingreconsidered may become a fairly complex matter, especially asone reconsiders more extensive elements in one’s prior plans. Butthis should not be taken to show that one may rationally proceedwithout adjusting one’s beliefs as one reconsiders. Rather, it showsjust how complicated — and so, costly — reconsideration of priorintentions can be.”
[Bratman, pg. 63, my emphasis]
Eric Pacuit
![Page 175: Logics of Rational Agencyepacuit/lograt/nasslli2010/lograt-lec5a… · Logics of Rational Agency Lecture 5 Eric Pacuit Tilburg Institute for Logic and Philosophy of Science Tilburg](https://reader035.fdocuments.us/reader035/viewer/2022071410/6105aaf24d2ece0ae545431e/html5/thumbnails/175.jpg)
Belief-Intention States: Beliefs
ϕ := pt | pre(a)t | post(a)t | Do(a)t | ϕ | ϕ ∧ ϕ | ¬ϕ
p ∈ At, a ∈ Act, t ∈ Z+
I pt means p is true at time t
I For every a and time t associate pre(a)t , post(a)t+1, whichwe treat as distinguished propositional variables
I Do(a)t mean the agent does a at t units from now
I is historic necessity
Eric Pacuit
![Page 176: Logics of Rational Agencyepacuit/lograt/nasslli2010/lograt-lec5a… · Logics of Rational Agency Lecture 5 Eric Pacuit Tilburg Institute for Logic and Philosophy of Science Tilburg](https://reader035.fdocuments.us/reader035/viewer/2022071410/6105aaf24d2ece0ae545431e/html5/thumbnails/176.jpg)
Belief-Intention States: Beliefs
Beliefs are consistent and deductively closed sets of formulas:
1. Propositional Tautologies;
2. S5 axiom schemes for : ((ϕ→ ψ)→ ϕ→ ψ,ϕ→ ϕ, ϕ→ ϕ,♦ϕ→ ♦ϕ, Necessitation);
3.∨
a∈Act Do(a)t ;
4. Do(a)t →∧
b 6=a ¬Do(b)t ;
5. Do(a)t → post(a)t+1;
6. pre(a)t → ♦Do(a)t ;
7. Modus Ponens
Eric Pacuit
![Page 177: Logics of Rational Agencyepacuit/lograt/nasslli2010/lograt-lec5a… · Logics of Rational Agency Lecture 5 Eric Pacuit Tilburg Institute for Logic and Philosophy of Science Tilburg](https://reader035.fdocuments.us/reader035/viewer/2022071410/6105aaf24d2ece0ae545431e/html5/thumbnails/177.jpg)
Belief-Intention States: Beliefs
Beliefs are consistent and deductively closed sets of formulas:
1. Propositional Tautologies;
2. S5 axiom schemes for : ((ϕ→ ψ)→ ϕ→ ψ,ϕ→ ϕ, ϕ→ ϕ,♦ϕ→ ♦ϕ, Necessitation);
3.∨
a∈Act Do(a)t ;
4. Do(a)t →∧
b 6=a ¬Do(b)t ;
5. Do(a)t → post(a)t+1;
6. pre(a)t → ♦Do(a)t ;
7. Modus Ponens
Eric Pacuit
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Belief-Intention States: Semantics
P = P(Prop ∪ pre(a), post(a) | a ∈ Act)
Path: π : Z→ (P × Act)
Eric Pacuit
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−1 0 t t + 1 t + 2 t + 3
π
π′
π′′
Eric Pacuit
![Page 180: Logics of Rational Agencyepacuit/lograt/nasslli2010/lograt-lec5a… · Logics of Rational Agency Lecture 5 Eric Pacuit Tilburg Institute for Logic and Philosophy of Science Tilburg](https://reader035.fdocuments.us/reader035/viewer/2022071410/6105aaf24d2ece0ae545431e/html5/thumbnails/180.jpg)
−1 0 t t + 1 t + 2 t + 3
π
π′
π′′
Eric Pacuit
![Page 181: Logics of Rational Agencyepacuit/lograt/nasslli2010/lograt-lec5a… · Logics of Rational Agency Lecture 5 Eric Pacuit Tilburg Institute for Logic and Philosophy of Science Tilburg](https://reader035.fdocuments.us/reader035/viewer/2022071410/6105aaf24d2ece0ae545431e/html5/thumbnails/181.jpg)
−1 0 t t + 1 t + 2 t + 3
π
π′
π′′
p, q, . . .
pre(a), pre(a′), . . .
post(b), post(b′), . . .
a
(π1(t), π(t)2)
Eric Pacuit
![Page 182: Logics of Rational Agencyepacuit/lograt/nasslli2010/lograt-lec5a… · Logics of Rational Agency Lecture 5 Eric Pacuit Tilburg Institute for Logic and Philosophy of Science Tilburg](https://reader035.fdocuments.us/reader035/viewer/2022071410/6105aaf24d2ece0ae545431e/html5/thumbnails/182.jpg)
−1 0 t t + 1 t + 2 t + 3
π
π′
π′′
p, q, . . .
pre(a), pre(a′), . . .
post(b), post(b′), . . .
π1(t)a
Eric Pacuit
![Page 183: Logics of Rational Agencyepacuit/lograt/nasslli2010/lograt-lec5a… · Logics of Rational Agency Lecture 5 Eric Pacuit Tilburg Institute for Logic and Philosophy of Science Tilburg](https://reader035.fdocuments.us/reader035/viewer/2022071410/6105aaf24d2ece0ae545431e/html5/thumbnails/183.jpg)
Belief-Intention States: Semantics
P = P(Prop ∪ pre(a), post(a) | a ∈ Act)
Path: π : Z→ (P × Act)
Historic necessity: π ∼t π′ iff for all t ′ ≤ t, π(t ′) = π′(t ′)
Appropriate path:
I If π(t)2 = a then post(a) ∈ π(t + 1)1
I If pre(a) ∈ π(t)1 then there is some π′ ∼t π such thatπ′(t)2 = a.
Eric Pacuit
![Page 184: Logics of Rational Agencyepacuit/lograt/nasslli2010/lograt-lec5a… · Logics of Rational Agency Lecture 5 Eric Pacuit Tilburg Institute for Logic and Philosophy of Science Tilburg](https://reader035.fdocuments.us/reader035/viewer/2022071410/6105aaf24d2ece0ae545431e/html5/thumbnails/184.jpg)
Belief-Intention States: Semantics
P = P(Prop ∪ pre(a), post(a) | a ∈ Act)
Path: π : Z→ (P × Act)
Historic necessity: π ∼t π′ iff for all t ′ ≤ t, π(t ′) = π′(t ′)
Appropriate path:
I If π(t)2 = a then post(a) ∈ π(t + 1)1
I If pre(a) ∈ π(t)1 then there is some π′ ∼t π such thatπ′(t)2 = a.
Eric Pacuit
![Page 185: Logics of Rational Agencyepacuit/lograt/nasslli2010/lograt-lec5a… · Logics of Rational Agency Lecture 5 Eric Pacuit Tilburg Institute for Logic and Philosophy of Science Tilburg](https://reader035.fdocuments.us/reader035/viewer/2022071410/6105aaf24d2ece0ae545431e/html5/thumbnails/185.jpg)
Belief-Intention States: Semantics
P = P(Prop ∪ pre(a), post(a) | a ∈ Act)
Path: π : Z→ (P × Act)
Historic necessity: π ∼t π′ iff for all t ′ ≤ t, π(t ′) = π′(t ′)
Appropriate path:
I If π(t)2 = a then post(a) ∈ π(t + 1)1
I If pre(a) ∈ π(t)1 then there is some π′ ∼t π such thatπ′(t)2 = a.
Eric Pacuit
![Page 186: Logics of Rational Agencyepacuit/lograt/nasslli2010/lograt-lec5a… · Logics of Rational Agency Lecture 5 Eric Pacuit Tilburg Institute for Logic and Philosophy of Science Tilburg](https://reader035.fdocuments.us/reader035/viewer/2022071410/6105aaf24d2ece0ae545431e/html5/thumbnails/186.jpg)
−1 0 t t + 1 t + 2 t + 3
π
π′
π′′
p, q, . . .
pre(a), pre(a′), . . .
post(b), post(b′), . . .
π1(t)a
Eric Pacuit
![Page 187: Logics of Rational Agencyepacuit/lograt/nasslli2010/lograt-lec5a… · Logics of Rational Agency Lecture 5 Eric Pacuit Tilburg Institute for Logic and Philosophy of Science Tilburg](https://reader035.fdocuments.us/reader035/viewer/2022071410/6105aaf24d2ece0ae545431e/html5/thumbnails/187.jpg)
−1 0 t t + 1 t + 2 t + 3
π
π′
π′′
p, q, . . .
pre(a), pre(a′), . . .
post(b), post(b′), . . .
p, q, . . .
pre(c), pre(c ′), . . .
post(a), post(d ′), . . .
π1(t)a
π1(t + 1)
Eric Pacuit
![Page 188: Logics of Rational Agencyepacuit/lograt/nasslli2010/lograt-lec5a… · Logics of Rational Agency Lecture 5 Eric Pacuit Tilburg Institute for Logic and Philosophy of Science Tilburg](https://reader035.fdocuments.us/reader035/viewer/2022071410/6105aaf24d2ece0ae545431e/html5/thumbnails/188.jpg)
−1 0 t t + 1 t + 2 t + 3
[π]t
π′
π′′
p, q, . . .
pre(a), pre(a′), . . .
post(b), post(b′), . . .
π1(t)a
a′
Eric Pacuit
![Page 189: Logics of Rational Agencyepacuit/lograt/nasslli2010/lograt-lec5a… · Logics of Rational Agency Lecture 5 Eric Pacuit Tilburg Institute for Logic and Philosophy of Science Tilburg](https://reader035.fdocuments.us/reader035/viewer/2022071410/6105aaf24d2ece0ae545431e/html5/thumbnails/189.jpg)
−1 0 t t + 1 t + 2 t + 3
[π]t
π′
π′′
p, q, . . .
pre(a), pre(a′), . . .
post(b), post(b′), . . .
cπ1(t)a
a′
Eric Pacuit
![Page 190: Logics of Rational Agencyepacuit/lograt/nasslli2010/lograt-lec5a… · Logics of Rational Agency Lecture 5 Eric Pacuit Tilburg Institute for Logic and Philosophy of Science Tilburg](https://reader035.fdocuments.us/reader035/viewer/2022071410/6105aaf24d2ece0ae545431e/html5/thumbnails/190.jpg)
Belief-Intention States: Semantics
Truth:
I π, t |= αt′ iff α ∈ π(t ′)1 for α = p, pre(a), post(a)
I π, t |= Do(a)t′ iff π(t ′)2 = a
I π, t |= ϕ iff for all π′ ∼t π, π′, t |= ϕ
I ....
Completeness Theorem. The logic given earlier is sound andcomplete with respect to the class of all appropriate paths.
Proof. Standard modal reasoning.
Eric Pacuit
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Belief-Intention States: Semantics
Truth:
I π, t |= αt′ iff α ∈ π(t ′)1 for α = p, pre(a), post(a)
I π, t |= Do(a)t′ iff π(t ′)2 = a
I π, t |= ϕ iff for all π′ ∼t π, π′, t |= ϕ
I ....
Completeness Theorem. The logic given earlier is sound andcomplete with respect to the class of all appropriate paths.
Proof. Standard modal reasoning.
Eric Pacuit
![Page 192: Logics of Rational Agencyepacuit/lograt/nasslli2010/lograt-lec5a… · Logics of Rational Agency Lecture 5 Eric Pacuit Tilburg Institute for Logic and Philosophy of Science Tilburg](https://reader035.fdocuments.us/reader035/viewer/2022071410/6105aaf24d2ece0ae545431e/html5/thumbnails/192.jpg)
Belief-Intention States: Instructions
There are “instructions” from the Planner about future choicesthat the agent agrees (promises, commits) to follow (if he can).
These instructions may
1. be a complete plan: for each (future) moment specify asingle action a ∈ Act the agent will perform.
2. be a partial plan: finite set of pairs (a, t) with a ∈ Act, t ∈ N.
3. be a conditional plan: do a at time t provided ϕ is true.
4. restrict available choices (rather than instructing the agent tofollow a specific plan), i.e., disjunctive plans.
5. be a more complicated structure (subplans, goals, etc.)
Eric Pacuit
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Belief-Intention States: Instructions
There are “instructions” from the Planner about future choicesthat the agent agrees (promises, commits) to follow (if he can).
These instructions may
1. be a complete plan: for each (future) moment specify asingle action a ∈ Act the agent will perform.
2. be a partial plan: finite set of pairs (a, t) with a ∈ Act, t ∈ N.
3. be a conditional plan: do a at time t provided ϕ is true.
4. restrict available choices (rather than instructing the agent tofollow a specific plan), i.e., disjunctive plans.
5. be a more complicated structure (subplans, goals, etc.)
Eric Pacuit
![Page 194: Logics of Rational Agencyepacuit/lograt/nasslli2010/lograt-lec5a… · Logics of Rational Agency Lecture 5 Eric Pacuit Tilburg Institute for Logic and Philosophy of Science Tilburg](https://reader035.fdocuments.us/reader035/viewer/2022071410/6105aaf24d2ece0ae545431e/html5/thumbnails/194.jpg)
Belief-Intention States: Instructions
There are “instructions” from the Planner about future choicesthat the agent agrees (promises, commits) to follow (if he can).
These instructions may
1. be a complete plan: for each (future) moment specify asingle action a ∈ Act the agent will perform.
2. be a partial plan: finite set of pairs (a, t) with a ∈ Act, t ∈ N.
3. be a conditional plan: do a at time t provided ϕ is true.
4. restrict available choices (rather than instructing the agent tofollow a specific plan), i.e., disjunctive plans.
5. be a more complicated structure (subplans, goals, etc.)
Eric Pacuit
![Page 195: Logics of Rational Agencyepacuit/lograt/nasslli2010/lograt-lec5a… · Logics of Rational Agency Lecture 5 Eric Pacuit Tilburg Institute for Logic and Philosophy of Science Tilburg](https://reader035.fdocuments.us/reader035/viewer/2022071410/6105aaf24d2ece0ae545431e/html5/thumbnails/195.jpg)
Belief-Intention States: Instructions
There are “instructions” from the Planner about future choicesthat the agent agrees (promises, commits) to follow (if he can).
These instructions may
1. be a complete plan: for each (future) moment specify asingle action a ∈ Act the agent will perform.
2. be a partial plan: finite set of pairs (a, t) with a ∈ Act, t ∈ N.
3. be a conditional plan: do a at time t provided ϕ is true.
4. restrict available choices (rather than instructing the agent tofollow a specific plan), i.e., disjunctive plans.
5. be a more complicated structure (subplans, goals, etc.)
Eric Pacuit
![Page 196: Logics of Rational Agencyepacuit/lograt/nasslli2010/lograt-lec5a… · Logics of Rational Agency Lecture 5 Eric Pacuit Tilburg Institute for Logic and Philosophy of Science Tilburg](https://reader035.fdocuments.us/reader035/viewer/2022071410/6105aaf24d2ece0ae545431e/html5/thumbnails/196.jpg)
Belief-Intention States: Instructions
There are “instructions” from the Planner about future choicesthat the agent agrees (promises, commits) to follow (if he can).
These instructions may
1. be a complete plan: for each (future) moment specify asingle action a ∈ Act the agent will perform.
2. be a partial plan: finite set of pairs (a, t) with a ∈ Act, t ∈ N.
3. be a conditional plan: do a at time t provided ϕ is true.
4. restrict available choices (rather than instructing the agent tofollow a specific plan), i.e., disjunctive plans.
5. be a more complicated structure (subplans, goals, etc.)
Eric Pacuit
![Page 197: Logics of Rational Agencyepacuit/lograt/nasslli2010/lograt-lec5a… · Logics of Rational Agency Lecture 5 Eric Pacuit Tilburg Institute for Logic and Philosophy of Science Tilburg](https://reader035.fdocuments.us/reader035/viewer/2022071410/6105aaf24d2ece0ae545431e/html5/thumbnails/197.jpg)
Belief-Intention States: Instructions
There are “instructions” from the Planner about future choicesthat the agent agrees (promises, commits) to follow (if he can).
These instructions may
1. be a complete plan: for each (future) moment specify asingle action a ∈ Act the agent will perform.
2. be a partial plan: finite set of pairs (a, t) with a ∈ Act, t ∈ N.
3. be a conditional plan: do a at time t provided ϕ is true.
4. restrict available choices (rather than instructing the agent tofollow a specific plan), i.e., disjunctive plans.
5. be a more complicated structure (subplans, goals, etc.)
Eric Pacuit
![Page 198: Logics of Rational Agencyepacuit/lograt/nasslli2010/lograt-lec5a… · Logics of Rational Agency Lecture 5 Eric Pacuit Tilburg Institute for Logic and Philosophy of Science Tilburg](https://reader035.fdocuments.us/reader035/viewer/2022071410/6105aaf24d2ece0ae545431e/html5/thumbnails/198.jpg)
Belief-Intention States: Instructions
There are “instructions” from the Planner about future choicesthat the agent agrees (promises, commits) to follow (if he can).
These instructions may
1. be a complete plan: for each (future) moment specify asingle action a ∈ Act the agent will perform.
2. be a partial plan: finite set of pairs (a, t) with a ∈ Act, t ∈ N.
3. be a conditional plan: do a at time t provided ϕ is true.
4. restrict available choices (rather than instructing the agent tofollow a specific plan), i.e., disjunctive plans.
5. be a more complicated structure (subplans, goals, etc.)
Eric Pacuit
![Page 199: Logics of Rational Agencyepacuit/lograt/nasslli2010/lograt-lec5a… · Logics of Rational Agency Lecture 5 Eric Pacuit Tilburg Institute for Logic and Philosophy of Science Tilburg](https://reader035.fdocuments.us/reader035/viewer/2022071410/6105aaf24d2ece0ae545431e/html5/thumbnails/199.jpg)
Belief-Intention Base: Coherence
A belief-intention base is a pair (B, I ) where 1. B is a set ofbeliefs and 2. I is a finite set of pairs (a, t)
Coherence: CohereI := ♦∧
(a,t)∈I pre(a)t
I (B, I ) is coherent if ¬CohereI 6∈ B.
I (Π, I ) is coherent if there is some π ∈ Π such thatπ, 0 |= CohereI .
Eric Pacuit
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Belief-Intention Base: Coherence
A belief-intention base is a pair (B, I ) where 1. B is a set ofbeliefs and 2. I is a finite set of pairs (a, t)
Coherence: CohereI := ♦∧
(a,t)∈I pre(a)t
I (B, I ) is coherent if ¬CohereI 6∈ B.
I (Π, I ) is coherent if there is some π ∈ Π such thatπ, 0 |= CohereI .
Eric Pacuit
![Page 201: Logics of Rational Agencyepacuit/lograt/nasslli2010/lograt-lec5a… · Logics of Rational Agency Lecture 5 Eric Pacuit Tilburg Institute for Logic and Philosophy of Science Tilburg](https://reader035.fdocuments.us/reader035/viewer/2022071410/6105aaf24d2ece0ae545431e/html5/thumbnails/201.jpg)
1. How should we describe the “mental state”?Sufficiently rich structure/(modal) language
2. What is a coherent description?What properties/logic characterize a rational balance?
3. What are the inputs?Consistent propositional formula
4. How should we characterize the revision operator?AGM postulates, Dynamic Doxastic Logic
Eric Pacuit
![Page 202: Logics of Rational Agencyepacuit/lograt/nasslli2010/lograt-lec5a… · Logics of Rational Agency Lecture 5 Eric Pacuit Tilburg Institute for Logic and Philosophy of Science Tilburg](https://reader035.fdocuments.us/reader035/viewer/2022071410/6105aaf24d2ece0ae545431e/html5/thumbnails/202.jpg)
Sources of Dynamics
1. Nature can reveal (true) facts about the current choicesituation (eg., facts that are true, choices that areavailable/not available in the future).
2. The agent can decide to perform an action (which in turnforces Nature to reveal certain information such as whichactions become available).
3. The Planner can amend the agent’s current set of instructions.
Typically only doing an action moves “time” forward. However, allthree may change the agent’s beliefs and current instructions.
Eric Pacuit
![Page 203: Logics of Rational Agencyepacuit/lograt/nasslli2010/lograt-lec5a… · Logics of Rational Agency Lecture 5 Eric Pacuit Tilburg Institute for Logic and Philosophy of Science Tilburg](https://reader035.fdocuments.us/reader035/viewer/2022071410/6105aaf24d2ece0ae545431e/html5/thumbnails/203.jpg)
Sources of Dynamics
1. Nature can reveal (true) facts about the current choicesituation (eg., facts that are true, choices that areavailable/not available in the future).
2. The agent can decide to perform an action (which in turnforces Nature to reveal certain information such as whichactions become available).
3. The Planner can amend the agent’s current set of instructions.
Typically only doing an action moves “time” forward. However, allthree may change the agent’s beliefs and current instructions.
Eric Pacuit
![Page 204: Logics of Rational Agencyepacuit/lograt/nasslli2010/lograt-lec5a… · Logics of Rational Agency Lecture 5 Eric Pacuit Tilburg Institute for Logic and Philosophy of Science Tilburg](https://reader035.fdocuments.us/reader035/viewer/2022071410/6105aaf24d2ece0ae545431e/html5/thumbnails/204.jpg)
Sources of Dynamics
1. Nature can reveal (true) facts about the current choicesituation (eg., facts that are true, choices that areavailable/not available in the future).
2. The agent can decide to perform an action (which in turnforces Nature to reveal certain information such as whichactions become available).
3. The Planner can amend the agent’s current set of instructions.
Typically only doing an action moves “time” forward. However, allthree may change the agent’s beliefs and current instructions.
Eric Pacuit
![Page 205: Logics of Rational Agencyepacuit/lograt/nasslli2010/lograt-lec5a… · Logics of Rational Agency Lecture 5 Eric Pacuit Tilburg Institute for Logic and Philosophy of Science Tilburg](https://reader035.fdocuments.us/reader035/viewer/2022071410/6105aaf24d2ece0ae545431e/html5/thumbnails/205.jpg)
Sources of Dynamics
1. Nature can reveal (true) facts about the current choicesituation (eg., facts that are true, choices that areavailable/not available in the future).
2. The agent can decide to perform an action (which in turnforces Nature to reveal certain information such as whichactions become available).
3. The Planner can amend the agent’s current set of instructions.
Typically only doing an action moves “time” forward. However, allthree may change the agent’s beliefs and current instructions.
Eric Pacuit
![Page 206: Logics of Rational Agencyepacuit/lograt/nasslli2010/lograt-lec5a… · Logics of Rational Agency Lecture 5 Eric Pacuit Tilburg Institute for Logic and Philosophy of Science Tilburg](https://reader035.fdocuments.us/reader035/viewer/2022071410/6105aaf24d2ece0ae545431e/html5/thumbnails/206.jpg)
Sources of Dynamics
1. Nature can reveal (true) facts about the current choicesituation (eg., facts that are true, choices that areavailable/not available in the future).
2. The agent can decide to perform an action (which in turnforces Nature to reveal certain information such as whichactions become available).
3. The Planner can amend the agent’s current set of instructions.
Typically only doing an action moves “time” forward. However, allthree may change the agent’s beliefs and current instructions.
Eric Pacuit
![Page 207: Logics of Rational Agencyepacuit/lograt/nasslli2010/lograt-lec5a… · Logics of Rational Agency Lecture 5 Eric Pacuit Tilburg Institute for Logic and Philosophy of Science Tilburg](https://reader035.fdocuments.us/reader035/viewer/2022071410/6105aaf24d2ece0ae545431e/html5/thumbnails/207.jpg)
The Revision Problem
1. How should we describe the “mental state”?Sufficiently rich structure/(modal) language
2. What is a coherent description?What properties/logic characterize a rational balance?
3. What are the inputs?Formulas and new plans
4. How should we characterize the revision operator?AGM postulates, Dynamic Doxastic Logic
Eric Pacuit
![Page 208: Logics of Rational Agencyepacuit/lograt/nasslli2010/lograt-lec5a… · Logics of Rational Agency Lecture 5 Eric Pacuit Tilburg Institute for Logic and Philosophy of Science Tilburg](https://reader035.fdocuments.us/reader035/viewer/2022071410/6105aaf24d2ece0ae545431e/html5/thumbnails/208.jpg)
The Revision Problem
−1 0 t t + 1 t + 2 t + 3
[π]t
π′
π′′
y
x
a
a
a′
b
a′
b
b′
b′
d
d ′
f
f
f
Eric Pacuit
![Page 209: Logics of Rational Agencyepacuit/lograt/nasslli2010/lograt-lec5a… · Logics of Rational Agency Lecture 5 Eric Pacuit Tilburg Institute for Logic and Philosophy of Science Tilburg](https://reader035.fdocuments.us/reader035/viewer/2022071410/6105aaf24d2ece0ae545431e/html5/thumbnails/209.jpg)
The Revision Problem
−1 0 t t + 1 t + 2 t + 3
[π]t
π′
π′′
y
x
a
a
a′
b
a′
b
b′
b′
d
d ′
f
f
f
I = (a, t), (b, t +1)
Eric Pacuit
![Page 210: Logics of Rational Agencyepacuit/lograt/nasslli2010/lograt-lec5a… · Logics of Rational Agency Lecture 5 Eric Pacuit Tilburg Institute for Logic and Philosophy of Science Tilburg](https://reader035.fdocuments.us/reader035/viewer/2022071410/6105aaf24d2ece0ae545431e/html5/thumbnails/210.jpg)
The Revision Problem
−1 0 t t + 1 t + 2 t + 3
[π]t
π′
π′′
y
x
a
a
a′
b
a′
b
b′
b′
d
d ′
f
f
f
I = (a, t), (b, t +1)
add Do(f )t+2
Eric Pacuit
![Page 211: Logics of Rational Agencyepacuit/lograt/nasslli2010/lograt-lec5a… · Logics of Rational Agency Lecture 5 Eric Pacuit Tilburg Institute for Logic and Philosophy of Science Tilburg](https://reader035.fdocuments.us/reader035/viewer/2022071410/6105aaf24d2ece0ae545431e/html5/thumbnails/211.jpg)
The Revision Problem
−1 0 t t + 1 t + 2 t + 3
[π]t
π′
π′′
y
x
a
a
a′
b
a′
b
b′
b′
d
d ′
f
f
f
I = (a, t), (b, t +1)
add Do(f )t+2
Eric Pacuit
![Page 212: Logics of Rational Agencyepacuit/lograt/nasslli2010/lograt-lec5a… · Logics of Rational Agency Lecture 5 Eric Pacuit Tilburg Institute for Logic and Philosophy of Science Tilburg](https://reader035.fdocuments.us/reader035/viewer/2022071410/6105aaf24d2ece0ae545431e/html5/thumbnails/212.jpg)
The Revision Problem
Let (B, I ) be a coherent belief-intention base.
In general, afterrevising by ϕ, the constraint of coherence may force a choicebetween any subset of I (including ∅).
Which element of P(I ) “should” be the new plan? Depends onmany features of the plan not represented in the currentframework: subplan structure, goals, costs, etc.
Intention revision: what is the difference between “add Do(a)t”and “add (a, t) to I ”?
Eric Pacuit
![Page 213: Logics of Rational Agencyepacuit/lograt/nasslli2010/lograt-lec5a… · Logics of Rational Agency Lecture 5 Eric Pacuit Tilburg Institute for Logic and Philosophy of Science Tilburg](https://reader035.fdocuments.us/reader035/viewer/2022071410/6105aaf24d2ece0ae545431e/html5/thumbnails/213.jpg)
The Revision Problem
Let (B, I ) be a coherent belief-intention base. In general, afterrevising by ϕ, the constraint of coherence may force a choicebetween any subset of I (including ∅).
Which element of P(I ) “should” be the new plan? Depends onmany features of the plan not represented in the currentframework: subplan structure, goals, costs, etc.
Intention revision: what is the difference between “add Do(a)t”and “add (a, t) to I ”?
Eric Pacuit
![Page 214: Logics of Rational Agencyepacuit/lograt/nasslli2010/lograt-lec5a… · Logics of Rational Agency Lecture 5 Eric Pacuit Tilburg Institute for Logic and Philosophy of Science Tilburg](https://reader035.fdocuments.us/reader035/viewer/2022071410/6105aaf24d2ece0ae545431e/html5/thumbnails/214.jpg)
The Revision Problem
Let (B, I ) be a coherent belief-intention base. In general, afterrevising by ϕ, the constraint of coherence may force a choicebetween any subset of I (including ∅).
Which element of P(I ) “should” be the new plan?
Depends onmany features of the plan not represented in the currentframework: subplan structure, goals, costs, etc.
Intention revision: what is the difference between “add Do(a)t”and “add (a, t) to I ”?
Eric Pacuit
![Page 215: Logics of Rational Agencyepacuit/lograt/nasslli2010/lograt-lec5a… · Logics of Rational Agency Lecture 5 Eric Pacuit Tilburg Institute for Logic and Philosophy of Science Tilburg](https://reader035.fdocuments.us/reader035/viewer/2022071410/6105aaf24d2ece0ae545431e/html5/thumbnails/215.jpg)
The Revision Problem
Let (B, I ) be a coherent belief-intention base. In general, afterrevising by ϕ, the constraint of coherence may force a choicebetween any subset of I (including ∅).
Which element of P(I ) “should” be the new plan? Depends onmany features of the plan not represented in the currentframework: subplan structure, goals, costs, etc.
Intention revision: what is the difference between “add Do(a)t”and “add (a, t) to I ”?
Eric Pacuit
![Page 216: Logics of Rational Agencyepacuit/lograt/nasslli2010/lograt-lec5a… · Logics of Rational Agency Lecture 5 Eric Pacuit Tilburg Institute for Logic and Philosophy of Science Tilburg](https://reader035.fdocuments.us/reader035/viewer/2022071410/6105aaf24d2ece0ae545431e/html5/thumbnails/216.jpg)
The Revision Problem
Let (B, I ) be a coherent belief-intention base. In general, afterrevising by ϕ, the constraint of coherence may force a choicebetween any subset of I (including ∅).
Which element of P(I ) “should” be the new plan? Depends onmany features of the plan not represented in the currentframework: subplan structure, goals, costs, etc.
Intention revision: what is the difference between “add Do(a)t”and “add (a, t) to I ”?
Eric Pacuit
![Page 217: Logics of Rational Agencyepacuit/lograt/nasslli2010/lograt-lec5a… · Logics of Rational Agency Lecture 5 Eric Pacuit Tilburg Institute for Logic and Philosophy of Science Tilburg](https://reader035.fdocuments.us/reader035/viewer/2022071410/6105aaf24d2ece0ae545431e/html5/thumbnails/217.jpg)
The Revision Problem
(B , I ) ? x = (B ′, I ′)Coherent Coherent
(a, t) ϕ
AGM Revision: ∗ Intention Revision: a
Eric Pacuit
![Page 218: Logics of Rational Agencyepacuit/lograt/nasslli2010/lograt-lec5a… · Logics of Rational Agency Lecture 5 Eric Pacuit Tilburg Institute for Logic and Philosophy of Science Tilburg](https://reader035.fdocuments.us/reader035/viewer/2022071410/6105aaf24d2ece0ae545431e/html5/thumbnails/218.jpg)
The Revision Problem
(B , I ) ? x = (B ′, I ′)Coherent Coherent
(a, t) ϕ
AGM Revision: ∗ Intention Revision: a
Eric Pacuit
![Page 219: Logics of Rational Agencyepacuit/lograt/nasslli2010/lograt-lec5a… · Logics of Rational Agency Lecture 5 Eric Pacuit Tilburg Institute for Logic and Philosophy of Science Tilburg](https://reader035.fdocuments.us/reader035/viewer/2022071410/6105aaf24d2ece0ae545431e/html5/thumbnails/219.jpg)
The Revision Problem
(B , I ) ? x = (B ′, I ′)Coherent Coherent
(a, t) ϕ
AGM Revision: ∗ Intention Revision: a
Eric Pacuit
![Page 220: Logics of Rational Agencyepacuit/lograt/nasslli2010/lograt-lec5a… · Logics of Rational Agency Lecture 5 Eric Pacuit Tilburg Institute for Logic and Philosophy of Science Tilburg](https://reader035.fdocuments.us/reader035/viewer/2022071410/6105aaf24d2ece0ae545431e/html5/thumbnails/220.jpg)
The Revision Problem
(B , I ) ? x = (B ′, I ′)Coherent Coherent
(a, t) ϕ
AGM Revision: ∗ Intention Revision: a
Eric Pacuit
![Page 221: Logics of Rational Agencyepacuit/lograt/nasslli2010/lograt-lec5a… · Logics of Rational Agency Lecture 5 Eric Pacuit Tilburg Institute for Logic and Philosophy of Science Tilburg](https://reader035.fdocuments.us/reader035/viewer/2022071410/6105aaf24d2ece0ae545431e/html5/thumbnails/221.jpg)
The Revision Problem
(B , I ) ? x = (B ′, I ′)Coherent Coherent
(a, t) ϕ
AGM Revision: ∗ Intention Revision: a
Eric Pacuit
![Page 222: Logics of Rational Agencyepacuit/lograt/nasslli2010/lograt-lec5a… · Logics of Rational Agency Lecture 5 Eric Pacuit Tilburg Institute for Logic and Philosophy of Science Tilburg](https://reader035.fdocuments.us/reader035/viewer/2022071410/6105aaf24d2ece0ae545431e/html5/thumbnails/222.jpg)
The Revision Problem
(B , I ) ? x = (B ′, I ′)Coherent Coherent
(a, t) ϕ
AGM Revision: ∗ Intention Revision: a
Eric Pacuit
![Page 223: Logics of Rational Agencyepacuit/lograt/nasslli2010/lograt-lec5a… · Logics of Rational Agency Lecture 5 Eric Pacuit Tilburg Institute for Logic and Philosophy of Science Tilburg](https://reader035.fdocuments.us/reader035/viewer/2022071410/6105aaf24d2ece0ae545431e/html5/thumbnails/223.jpg)
Postulates: Adding an Intention
Suppose (B, I ) is coherent and (a, t) and action/time pair.
Intention Revision Operator: (B, I ) (a, t) = (B ′, I ′) where
1. (B ′, I ′) is coherent
2. If (B, (a, t)) is coherent then (a, t) ∈ I ′
3. If (B, I ∪ (a, t)) is coherent then I ∪ (a, t) ⊆ I ′
4. B ′ = B
Eric Pacuit
![Page 224: Logics of Rational Agencyepacuit/lograt/nasslli2010/lograt-lec5a… · Logics of Rational Agency Lecture 5 Eric Pacuit Tilburg Institute for Logic and Philosophy of Science Tilburg](https://reader035.fdocuments.us/reader035/viewer/2022071410/6105aaf24d2ece0ae545431e/html5/thumbnails/224.jpg)
Postulates: Adding an Intention
Suppose (B, I ) is coherent and (a, t) and action/time pair.
Intention Revision Operator: (B, I ) (a, t) = (B ′, I ′) where
1. (B ′, I ′) is coherent
2. If (B, (a, t)) is coherent then (a, t) ∈ I ′
3. If (B, I ∪ (a, t)) is coherent then I ∪ (a, t) ⊆ I ′
4. B ′ = B
Eric Pacuit
![Page 225: Logics of Rational Agencyepacuit/lograt/nasslli2010/lograt-lec5a… · Logics of Rational Agency Lecture 5 Eric Pacuit Tilburg Institute for Logic and Philosophy of Science Tilburg](https://reader035.fdocuments.us/reader035/viewer/2022071410/6105aaf24d2ece0ae545431e/html5/thumbnails/225.jpg)
Postulates: AGM Revision
Suppose (B, I ) is coherent and ϕ a consistent formula.
Let (B, I ) ? ϕ = (B ′, I ′) where
1. (B ′, I ′) = (B ′, I ) ε where satisfies the earlier postulates
2. ϕ ∈ B ′
3. If ¬ϕ 6∈ B then Cl(B ∪ ϕ) = B ′
4. If ϕ and ψ are equivalent and (B, I ) ∗ ψ = (B ′′, I ′′) thenB ′ = B ′′
5. B ′ = Cl(B ′)
6. If ¬ψ 6∈ B ′ and (B, I ) ∗ ψ = (B ′′, I ′′) then Cl(B ′ ∪ ψ) ⊆ B ′′
7. If (B, I ′′) ∗ ϕ = (B ′′, I ′′′) then B ′ = B ′′.
Eric Pacuit
![Page 226: Logics of Rational Agencyepacuit/lograt/nasslli2010/lograt-lec5a… · Logics of Rational Agency Lecture 5 Eric Pacuit Tilburg Institute for Logic and Philosophy of Science Tilburg](https://reader035.fdocuments.us/reader035/viewer/2022071410/6105aaf24d2ece0ae545431e/html5/thumbnails/226.jpg)
Postulates: AGM Revision
Suppose (B, I ) is coherent and ϕ a consistent formula.Let (B, I ) ? ϕ = (B ′, I ′) where
1. (B ′, I ′) = (B ′, I ) ε where satisfies the earlier postulates
2. ϕ ∈ B ′
3. If ¬ϕ 6∈ B then Cl(B ∪ ϕ) = B ′
4. If ϕ and ψ are equivalent and (B, I ) ∗ ψ = (B ′′, I ′′) thenB ′ = B ′′
5. B ′ = Cl(B ′)
6. If ¬ψ 6∈ B ′ and (B, I ) ∗ ψ = (B ′′, I ′′) then Cl(B ′ ∪ ψ) ⊆ B ′′
7. If (B, I ′′) ∗ ϕ = (B ′′, I ′′′) then B ′ = B ′′.
Eric Pacuit
![Page 227: Logics of Rational Agencyepacuit/lograt/nasslli2010/lograt-lec5a… · Logics of Rational Agency Lecture 5 Eric Pacuit Tilburg Institute for Logic and Philosophy of Science Tilburg](https://reader035.fdocuments.us/reader035/viewer/2022071410/6105aaf24d2ece0ae545431e/html5/thumbnails/227.jpg)
Postulates: AGM Revision
Suppose (B, I ) is coherent and ϕ a consistent formula.Let (B, I ) ? ϕ = (B ′, I ′) where
1. (B ′, I ′) = (B ′, I ) ε where satisfies the earlier postulates
2. ϕ ∈ B ′
3. If ¬ϕ 6∈ B then Cl(B ∪ ϕ) = B ′
4. If ϕ and ψ are equivalent and (B, I ) ∗ ψ = (B ′′, I ′′) thenB ′ = B ′′
5. B ′ = Cl(B ′)
6. If ¬ψ 6∈ B ′ and (B, I ) ∗ ψ = (B ′′, I ′′) then Cl(B ′ ∪ ψ) ⊆ B ′′
7. If (B, I ′′) ∗ ϕ = (B ′′, I ′′′) then B ′ = B ′′.
Eric Pacuit
![Page 228: Logics of Rational Agencyepacuit/lograt/nasslli2010/lograt-lec5a… · Logics of Rational Agency Lecture 5 Eric Pacuit Tilburg Institute for Logic and Philosophy of Science Tilburg](https://reader035.fdocuments.us/reader035/viewer/2022071410/6105aaf24d2ece0ae545431e/html5/thumbnails/228.jpg)
Modeling Revision
(Π, I ,≤, γ) is a belief intention model where
I Π is an appropriate set of paths
I ≤ is a total preorder on Π
I (min≤(Π), I ) is coherent
I γ is a selection function mapping triples (Π′, I ′, (a, t)) to Jwhere
• (Π′, J) is coherent• If (Π′, (a, t)) is coherent then (a, t) ∈ J• If (Π′, I ′ ∪ (a, t)) is coherent then J = I ′ ∪ (a, t)• J ⊆ I ′ ∪ (a, t)
Eric Pacuit
![Page 229: Logics of Rational Agencyepacuit/lograt/nasslli2010/lograt-lec5a… · Logics of Rational Agency Lecture 5 Eric Pacuit Tilburg Institute for Logic and Philosophy of Science Tilburg](https://reader035.fdocuments.us/reader035/viewer/2022071410/6105aaf24d2ece0ae545431e/html5/thumbnails/229.jpg)
Modeling Revision
(Π, I ,≤, γ) is a belief intention model where
Adding an intention: (Π, I ,≤, γ) (a, t) = (Π, I ′,≤, γ′) whereγ = γ′ and I ′ = γ(min(Π), I , (a, t))
Adding a belief: (Π, I ,≤, γ) ∗ ϕ = (Π, I ′,≤′, γ′) where γ = γ′, ≤′is the lexicographic re-ordering of ≤ by ϕ andI ′ = γ(min≤′(Π), I , ε).
Eric Pacuit
![Page 230: Logics of Rational Agencyepacuit/lograt/nasslli2010/lograt-lec5a… · Logics of Rational Agency Lecture 5 Eric Pacuit Tilburg Institute for Logic and Philosophy of Science Tilburg](https://reader035.fdocuments.us/reader035/viewer/2022071410/6105aaf24d2ece0ae545431e/html5/thumbnails/230.jpg)
Modeling Revision
(Π, I ,≤, γ) is a belief intention model where
Adding an intention: (Π, I ,≤, γ) (a, t) = (Π, I ′,≤, γ′) whereγ = γ′ and I ′ = γ(min(Π), I , (a, t))
Adding a belief: (Π, I ,≤, γ) ∗ ϕ = (Π, I ′,≤′, γ′) where γ = γ′, ≤′is the lexicographic re-ordering of ≤ by ϕ andI ′ = γ(min≤′(Π), I , ε).
Eric Pacuit
![Page 231: Logics of Rational Agencyepacuit/lograt/nasslli2010/lograt-lec5a… · Logics of Rational Agency Lecture 5 Eric Pacuit Tilburg Institute for Logic and Philosophy of Science Tilburg](https://reader035.fdocuments.us/reader035/viewer/2022071410/6105aaf24d2ece0ae545431e/html5/thumbnails/231.jpg)
Modeling Revision
(Π, I ,≤, γ) is a belief intention model where
Adding an intention: (Π, I ,≤, γ) (a, t) = (Π, I ′,≤, γ′) whereγ = γ′ and I ′ = γ(min(Π), I , (a, t))
Adding a belief: (Π, I ,≤, γ) ∗ ϕ = (Π, I ′,≤′, γ′) where γ = γ′, ≤′is the lexicographic re-ordering of ≤ by ϕ andI ′ = γ(min≤′(Π), I , ε).
Eric Pacuit
![Page 232: Logics of Rational Agencyepacuit/lograt/nasslli2010/lograt-lec5a… · Logics of Rational Agency Lecture 5 Eric Pacuit Tilburg Institute for Logic and Philosophy of Science Tilburg](https://reader035.fdocuments.us/reader035/viewer/2022071410/6105aaf24d2ece0ae545431e/html5/thumbnails/232.jpg)
Conclusions
1. How should we describe the “mental state”?Sufficiently rich structure/(modal) language
2. What is a coherent description?What properties/logic characterize a rational balance?
3. What are the inputs?Formulas and new plans
4. How should we characterize the revision operator?general postulates, dynamic modal operators
Eric Pacuit
![Page 233: Logics of Rational Agencyepacuit/lograt/nasslli2010/lograt-lec5a… · Logics of Rational Agency Lecture 5 Eric Pacuit Tilburg Institute for Logic and Philosophy of Science Tilburg](https://reader035.fdocuments.us/reader035/viewer/2022071410/6105aaf24d2ece0ae545431e/html5/thumbnails/233.jpg)
Conclusions
I Contingent beliefs: B I = Cl(B ∪ Do(a)t | (a, t) ∈ I). Wecan read off postulates.
I What is the precise relationship with existing BDI logics (eg.,DEL-style dynamics)? Example
I Complex plans (eg., conditional, disjunctive plans): what isthe appropriate notion of coherence?
I Iterated revision...
I Other mental attitudes...
Eric Pacuit
![Page 234: Logics of Rational Agencyepacuit/lograt/nasslli2010/lograt-lec5a… · Logics of Rational Agency Lecture 5 Eric Pacuit Tilburg Institute for Logic and Philosophy of Science Tilburg](https://reader035.fdocuments.us/reader035/viewer/2022071410/6105aaf24d2ece0ae545431e/html5/thumbnails/234.jpg)
Conclusions
I Contingent beliefs: B I = Cl(B ∪ Do(a)t | (a, t) ∈ I). Wecan read off postulates.
I What is the precise relationship with existing BDI logics (eg.,DEL-style dynamics)? Example
I Complex plans (eg., conditional, disjunctive plans): what isthe appropriate notion of coherence?
I Iterated revision...
I Other mental attitudes...
Eric Pacuit
![Page 235: Logics of Rational Agencyepacuit/lograt/nasslli2010/lograt-lec5a… · Logics of Rational Agency Lecture 5 Eric Pacuit Tilburg Institute for Logic and Philosophy of Science Tilburg](https://reader035.fdocuments.us/reader035/viewer/2022071410/6105aaf24d2ece0ae545431e/html5/thumbnails/235.jpg)
Conclusions
I Contingent beliefs: B I = Cl(B ∪ Do(a)t | (a, t) ∈ I). Wecan read off postulates.
I What is the precise relationship with existing BDI logics (eg.,DEL-style dynamics)? Example
I Complex plans (eg., conditional, disjunctive plans): what isthe appropriate notion of coherence?
I Iterated revision...
I Other mental attitudes...
Eric Pacuit
![Page 236: Logics of Rational Agencyepacuit/lograt/nasslli2010/lograt-lec5a… · Logics of Rational Agency Lecture 5 Eric Pacuit Tilburg Institute for Logic and Philosophy of Science Tilburg](https://reader035.fdocuments.us/reader035/viewer/2022071410/6105aaf24d2ece0ae545431e/html5/thumbnails/236.jpg)
Conclusions
I Contingent beliefs: B I = Cl(B ∪ Do(a)t | (a, t) ∈ I). Wecan read off postulates.
I What is the precise relationship with existing BDI logics (eg.,DEL-style dynamics)? Example
I Complex plans (eg., conditional, disjunctive plans): what isthe appropriate notion of coherence?
I Iterated revision...
I Other mental attitudes...
Eric Pacuit
![Page 237: Logics of Rational Agencyepacuit/lograt/nasslli2010/lograt-lec5a… · Logics of Rational Agency Lecture 5 Eric Pacuit Tilburg Institute for Logic and Philosophy of Science Tilburg](https://reader035.fdocuments.us/reader035/viewer/2022071410/6105aaf24d2ece0ae545431e/html5/thumbnails/237.jpg)
Conclusions
I Contingent beliefs: B I = Cl(B ∪ Do(a)t | (a, t) ∈ I). Wecan read off postulates.
I What is the precise relationship with existing BDI logics (eg.,DEL-style dynamics)? Example
I Complex plans (eg., conditional, disjunctive plans): what isthe appropriate notion of coherence?
I Iterated revision...
I Other mental attitudes...
Eric Pacuit
![Page 238: Logics of Rational Agencyepacuit/lograt/nasslli2010/lograt-lec5a… · Logics of Rational Agency Lecture 5 Eric Pacuit Tilburg Institute for Logic and Philosophy of Science Tilburg](https://reader035.fdocuments.us/reader035/viewer/2022071410/6105aaf24d2ece0ae545431e/html5/thumbnails/238.jpg)
ConclusionsWe are interested in reasoning about rational agents interacting insocial situations.
What do the logical frameworks contribute to the discussion onrational agency?
I Normative vs. Descriptive
I refine and test our intuitions: provide many answers to thequestion what is a rational agent?
I (epistemic) foundations of game theoryLogic and Game Theory, not Logic in place of Game Theory.
I Social Software: Verify properties of social procedures
• Refine existing social procedures or suggest new ones
R. Parikh. Social Software. Synthese 132 (2002).
Eric Pacuit
![Page 239: Logics of Rational Agencyepacuit/lograt/nasslli2010/lograt-lec5a… · Logics of Rational Agency Lecture 5 Eric Pacuit Tilburg Institute for Logic and Philosophy of Science Tilburg](https://reader035.fdocuments.us/reader035/viewer/2022071410/6105aaf24d2ece0ae545431e/html5/thumbnails/239.jpg)
ConclusionsWe are interested in reasoning about rational agents interacting insocial situations.
What do the logical frameworks contribute to the discussion onrational agency?
I Normative vs. Descriptive
I refine and test our intuitions: provide many answers to thequestion what is a rational agent?
I (epistemic) foundations of game theoryLogic and Game Theory, not Logic in place of Game Theory.
I Social Software: Verify properties of social procedures
• Refine existing social procedures or suggest new ones
R. Parikh. Social Software. Synthese 132 (2002).
Eric Pacuit
![Page 240: Logics of Rational Agencyepacuit/lograt/nasslli2010/lograt-lec5a… · Logics of Rational Agency Lecture 5 Eric Pacuit Tilburg Institute for Logic and Philosophy of Science Tilburg](https://reader035.fdocuments.us/reader035/viewer/2022071410/6105aaf24d2ece0ae545431e/html5/thumbnails/240.jpg)
ConclusionsWe are interested in reasoning about rational agents interacting insocial situations.
What do the logical frameworks contribute to the discussion onrational agency?
I Normative vs. Descriptive
I refine and test our intuitions: provide many answers to thequestion what is a rational agent?
I (epistemic) foundations of game theoryLogic and Game Theory, not Logic in place of Game Theory.
I Social Software: Verify properties of social procedures
• Refine existing social procedures or suggest new ones
R. Parikh. Social Software. Synthese 132 (2002).
Eric Pacuit
![Page 241: Logics of Rational Agencyepacuit/lograt/nasslli2010/lograt-lec5a… · Logics of Rational Agency Lecture 5 Eric Pacuit Tilburg Institute for Logic and Philosophy of Science Tilburg](https://reader035.fdocuments.us/reader035/viewer/2022071410/6105aaf24d2ece0ae545431e/html5/thumbnails/241.jpg)
ConclusionsWe are interested in reasoning about rational agents interacting insocial situations.
What do the logical frameworks contribute to the discussion onrational agency?
I Normative vs. Descriptive
I refine and test our intuitions: provide many answers to thequestion what is a rational agent?
I (epistemic) foundations of game theoryLogic and Game Theory, not Logic in place of Game Theory.
I Social Software: Verify properties of social procedures
• Refine existing social procedures or suggest new ones
R. Parikh. Social Software. Synthese 132 (2002).
Eric Pacuit
![Page 242: Logics of Rational Agencyepacuit/lograt/nasslli2010/lograt-lec5a… · Logics of Rational Agency Lecture 5 Eric Pacuit Tilburg Institute for Logic and Philosophy of Science Tilburg](https://reader035.fdocuments.us/reader035/viewer/2022071410/6105aaf24d2ece0ae545431e/html5/thumbnails/242.jpg)
ConclusionsWe are interested in reasoning about rational agents interacting insocial situations.
What do the logical frameworks contribute to the discussion onrational agency?
I Normative vs. Descriptive
I refine and test our intuitions: provide many answers to thequestion what is a rational agent?
I (epistemic) foundations of game theoryLogic and Game Theory, not Logic in place of Game Theory.
I Social Software: Verify properties of social procedures
• Refine existing social procedures or suggest new ones
R. Parikh. Social Software. Synthese 132 (2002).
Eric Pacuit
![Page 243: Logics of Rational Agencyepacuit/lograt/nasslli2010/lograt-lec5a… · Logics of Rational Agency Lecture 5 Eric Pacuit Tilburg Institute for Logic and Philosophy of Science Tilburg](https://reader035.fdocuments.us/reader035/viewer/2022071410/6105aaf24d2ece0ae545431e/html5/thumbnails/243.jpg)
ConclusionsWe are interested in reasoning about rational agents interacting insocial situations.
What do the logical frameworks contribute to the discussion onrational agency?
I Normative vs. Descriptive
I refine and test our intuitions: provide many answers to thequestion what is a rational agent?
I (epistemic) foundations of game theoryLogic and Game Theory, not Logic in place of Game Theory.
I Social Software: Verify properties of social procedures
• Refine existing social procedures or suggest new ones
R. Parikh. Social Software. Synthese 132 (2002).
Eric Pacuit
![Page 244: Logics of Rational Agencyepacuit/lograt/nasslli2010/lograt-lec5a… · Logics of Rational Agency Lecture 5 Eric Pacuit Tilburg Institute for Logic and Philosophy of Science Tilburg](https://reader035.fdocuments.us/reader035/viewer/2022071410/6105aaf24d2ece0ae545431e/html5/thumbnails/244.jpg)
Logics of Rational Agency: Conclusions
I Special issue of JOLLI: Temporal Logics of Agency (eds. J.van Benthem and EP)
I Special Issue of Synthese: Knowledge, Rationality andInteraction. Logic and Intelligent Interaction, Volume 169,Number 2 / July, 2009(eds. T. Agotnes, J. van Benthem and EP)
I New subarea of Stanford Encyclopedia of Philosophy on logicand rational agency(eds. J. van Benthem, EP, and O. Roy)
Eric Pacuit
![Page 245: Logics of Rational Agencyepacuit/lograt/nasslli2010/lograt-lec5a… · Logics of Rational Agency Lecture 5 Eric Pacuit Tilburg Institute for Logic and Philosophy of Science Tilburg](https://reader035.fdocuments.us/reader035/viewer/2022071410/6105aaf24d2ece0ae545431e/html5/thumbnails/245.jpg)
Thank You!
Eric Pacuit
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Dynamic Operator
[Recall a BDI state: Γ0 = 〈B0,D0, 〈I0,A0〉,P0〉Γ1 = 〈B1,D1, 〈I1,A1〉,P1〉]
Let Ω be a finite set of observations (ground or temporal formulas).
Γ0 −→Ω Γ1 iff:
1. B1 = B0 ∗AGM∧ω∈Ω ω (and not inconsistent)
2. A1 = activePlans(cleanup(B1,A0,D,P),B1,D,P)
3. I1 = Int(A1)
Eric Pacuit
![Page 247: Logics of Rational Agencyepacuit/lograt/nasslli2010/lograt-lec5a… · Logics of Rational Agency Lecture 5 Eric Pacuit Tilburg Institute for Logic and Philosophy of Science Tilburg](https://reader035.fdocuments.us/reader035/viewer/2022071410/6105aaf24d2ece0ae545431e/html5/thumbnails/247.jpg)
Dynamic Operator
[Recall a BDI state: Γ0 = 〈B0,D0, 〈I0,A0〉,P0〉Γ1 = 〈B1,D1, 〈I1,A1〉,P1〉]
Let Ω be a finite set of observations (ground or temporal formulas).
Γ0 −→Ω Γ1 iff:
1. B1 = B0 ∗AGM∧ω∈Ω ω (and not inconsistent)
2. A1 = activePlans(cleanup(B1,A0,D,P),B1,D,P)
3. I1 = Int(A1)
Eric Pacuit
![Page 248: Logics of Rational Agencyepacuit/lograt/nasslli2010/lograt-lec5a… · Logics of Rational Agency Lecture 5 Eric Pacuit Tilburg Institute for Logic and Philosophy of Science Tilburg](https://reader035.fdocuments.us/reader035/viewer/2022071410/6105aaf24d2ece0ae545431e/html5/thumbnails/248.jpg)
Dynamic Operator
[Recall a BDI state: Γ0 = 〈B0,D0, 〈I0,A0〉,P0〉Γ1 = 〈B1,D1, 〈I1,A1〉,P1〉]
Let Ω be a finite set of observations (ground or temporal formulas).
Γ0 −→Ω Γ1 iff:
1. B1 = B0 ∗AGM∧ω∈Ω ω (and not inconsistent)
2. A1 = activePlans(cleanup(B1,A0,D,P),B1,D,P)
3. I1 = Int(A1)
Eric Pacuit
![Page 249: Logics of Rational Agencyepacuit/lograt/nasslli2010/lograt-lec5a… · Logics of Rational Agency Lecture 5 Eric Pacuit Tilburg Institute for Logic and Philosophy of Science Tilburg](https://reader035.fdocuments.us/reader035/viewer/2022071410/6105aaf24d2ece0ae545431e/html5/thumbnails/249.jpg)
Dynamic Operator
[Recall a BDI state: Γ0 = 〈B0,D0, 〈I0,A0〉,P0〉Γ1 = 〈B1,D1, 〈I1,A1〉,P1〉]
Let Ω be a finite set of observations (ground or temporal formulas).
Γ0 −→Ω Γ1 iff:
1. B1 = B0 ∗AGM∧ω∈Ω ω (and not inconsistent)
2. A1 = activePlans(cleanup(B1,A0,D,P),B1,D,P)
3. I1 = Int(A1)
Eric Pacuit
![Page 250: Logics of Rational Agencyepacuit/lograt/nasslli2010/lograt-lec5a… · Logics of Rational Agency Lecture 5 Eric Pacuit Tilburg Institute for Logic and Philosophy of Science Tilburg](https://reader035.fdocuments.us/reader035/viewer/2022071410/6105aaf24d2ece0ae545431e/html5/thumbnails/250.jpg)
Derived Properties
I Versions of AGM postulates for beliefs: eg., [Ω]∧
w∈Ω Bω
I [Ω]Bϕ→ [Ω]¬Iϕ
I I∧ω∈Ω ω → ¬[Ω]⊥
I (Dϕ ∧ Iϕ ∧ ¬[Ω]Bϕ ∧ ¬[Ω]B¬ϕ)→ [Ω]Iϕ
Back to conclusions
Eric Pacuit
![Page 251: Logics of Rational Agencyepacuit/lograt/nasslli2010/lograt-lec5a… · Logics of Rational Agency Lecture 5 Eric Pacuit Tilburg Institute for Logic and Philosophy of Science Tilburg](https://reader035.fdocuments.us/reader035/viewer/2022071410/6105aaf24d2ece0ae545431e/html5/thumbnails/251.jpg)
Derived Properties
I Versions of AGM postulates for beliefs: eg., [Ω]∧
w∈Ω Bω
I [Ω]Bϕ→ [Ω]¬Iϕ
I I∧ω∈Ω ω → ¬[Ω]⊥
I (Dϕ ∧ Iϕ ∧ ¬[Ω]Bϕ ∧ ¬[Ω]B¬ϕ)→ [Ω]Iϕ
Back to conclusions
Eric Pacuit
![Page 252: Logics of Rational Agencyepacuit/lograt/nasslli2010/lograt-lec5a… · Logics of Rational Agency Lecture 5 Eric Pacuit Tilburg Institute for Logic and Philosophy of Science Tilburg](https://reader035.fdocuments.us/reader035/viewer/2022071410/6105aaf24d2ece0ae545431e/html5/thumbnails/252.jpg)
Derived Properties
I Versions of AGM postulates for beliefs: eg., [Ω]∧
w∈Ω Bω
I [Ω]Bϕ→ [Ω]¬Iϕ
I I∧ω∈Ω ω → ¬[Ω]⊥
I (Dϕ ∧ Iϕ ∧ ¬[Ω]Bϕ ∧ ¬[Ω]B¬ϕ)→ [Ω]Iϕ
Back to conclusions
Eric Pacuit
![Page 253: Logics of Rational Agencyepacuit/lograt/nasslli2010/lograt-lec5a… · Logics of Rational Agency Lecture 5 Eric Pacuit Tilburg Institute for Logic and Philosophy of Science Tilburg](https://reader035.fdocuments.us/reader035/viewer/2022071410/6105aaf24d2ece0ae545431e/html5/thumbnails/253.jpg)
Derived Properties
I Versions of AGM postulates for beliefs: eg., [Ω]∧
w∈Ω Bω
I [Ω]Bϕ→ [Ω]¬Iϕ
I I∧ω∈Ω ω → ¬[Ω]⊥
I (Dϕ ∧ Iϕ ∧ ¬[Ω]Bϕ ∧ ¬[Ω]B¬ϕ)→ [Ω]Iϕ
Back to conclusions
Eric Pacuit
![Page 254: Logics of Rational Agencyepacuit/lograt/nasslli2010/lograt-lec5a… · Logics of Rational Agency Lecture 5 Eric Pacuit Tilburg Institute for Logic and Philosophy of Science Tilburg](https://reader035.fdocuments.us/reader035/viewer/2022071410/6105aaf24d2ece0ae545431e/html5/thumbnails/254.jpg)
C & L Logic of Intention
1. Intentions normally pose problems for the agent; the agentneeds to determine a way to achieve them.
2. Intentions provide a “screen of admissibility” for adoptingother intentions.
3. Agents “track” the success of their attempts to achieve theirintentions.
4. If an agent intends to achieve p, then
4.1 The agent believes p is possible4.2 The agent does not believe he will not bring abut p4.3 Under certain conditions, the agent believes he will bring about
p4.4 Agents need not intend all the expected side-effects of their
intentions.
Eric Pacuit
![Page 255: Logics of Rational Agencyepacuit/lograt/nasslli2010/lograt-lec5a… · Logics of Rational Agency Lecture 5 Eric Pacuit Tilburg Institute for Logic and Philosophy of Science Tilburg](https://reader035.fdocuments.us/reader035/viewer/2022071410/6105aaf24d2ece0ae545431e/html5/thumbnails/255.jpg)
C & L Logic of Intention
(PGOALip) := (GOALi (LATERp)) ∧(BELi¬p)∧[BEFORE((BELip) ∨ (BELi¬p))¬(GOALi (LATERp))]
(INTENDia) := (PGOALi [DONEi (BELi (HAPPENSa))?; a])
Back
Eric Pacuit