A DYNAMIC ARGUMENTATION FRAMEWORK · 2017. 9. 1. · Dung’s AFs The most abstract viewpoint on...
Transcript of A DYNAMIC ARGUMENTATION FRAMEWORK · 2017. 9. 1. · Dung’s AFs The most abstract viewpoint on...
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A DYNAMIC ARGUMENTATION
FRAMEWORK
ND Rotstein, MO Moguillansky,AJ García, GR Simari
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The DAF, Introduction
Extension of Dung’s AFs
Representation of argumental structures
Modelling knowledge dynamics
AFs as an instance of a DAF
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Dung’s AFs
The most abstract viewpoint on argumentation
Simple yet meaningful
Suitable for grounding argumentation-based theoretical approaches
Main focus: argumentation semantics
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Why Another AF?
Composition of arguments (argumental substructures)
How to determine defeat (conflict + preference)
Consideration of evidence (dynamics)
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Evidence; Arguments
In the DAF:
Arguments have an interface: premises and claims
Arguments may chain: argumental structures
Arguments might not hold now: evidence
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Arguments
An argument A defined upon a domain language L:
pr(A) ! 2L, cl(A) ! L
cl(A) " pr(A)
cl(A) " pr(A)
Pieces of evidence also belong to L
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Coherency
A set of evidence is a consistent set of facts representing the current environment
Given a set ArgsL of arguments, the conflict relation ⋈:ArgsL×ArgsL # ⋈ # {(A,B) | cl(A) = cl(B) or cl(A) ! pr(B)}
Coherent argument wrt. a set E of evidence:(consistent) cl(A) " E, (non-redundant) cl(A) " E
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Active Arguments; Support
Aa b a b
c
A
B
xx
E = {a, b} E = {a, c}
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Active Arguments; Support
Aa b a b
c
A
B
xx
E = {a, b} E = {a, c}
support
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Active Arguments
a b cA B
x
E = {a, b, c}
b
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Argumental Structures
Trees of arguments linked from claims to premises
Each premise is supported by at most one argument
Top argument: top(S) - Set of arguments: args(S)
Claim: cl(S) - Premises: pr(S)
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Well-formed Arg. Structure
(Premise consistency) no a,b ! pr(S) s.t. a = b
(Consistency) no A,B s.t. A⋈B
(Non-circularity) if cl(B) ! pr(A) then A does not transitively support B
(Uniformity) if A supports B through b, then A supports every Bi with b as a premise
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Non-WF Arg. Structures, e.g.
b
a
¬a
c
c
a
b
a
b c
a
x b
b c
a
x b
y
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Non-WF Arg. Structures, e.g.
b
a
¬a
c
c
a
b
a
b c
a
x b
b c
a
x b
y
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Non-WF Arg. Structures, e.g.
b
a
¬a
c
c
a
b
a
b c
a
x b
b c
a
x b
y
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Non-WF Arg. Structures, e.g.
b
a
¬a
c
c
a
b
a
b c
a
x b
b c
a
x b
y
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Non-WF Arg. Structures, e.g.
b
a
¬a
c
c
a
b
a
b c
a
x b
b c
a
x b
y
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Conflict + Preference = Defeat
Si ⊑ S iff Si is a structure and args(Si) $ args(S)
S1 ≍ S2 iff top(S1) ⋈ top(S2)
Preference function pref(S1,S2) = [S1 | S2 | !]S1 % S2 iff Sk ⊑ S2, Sk ≍ S1 and pref(S1,Sk) = S1
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The Framework
DAF F = ⟨E, W, ⋈, pref⟩
E: current evidence
W: working set of arguments
⋈: conflict relation upon pairs of arguments
pref: function defined over pairs of arg. structures
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The DAF, e.g.
many_copsA2
good_security
thieves andpoor_security
A3
dangerous_route
underpaid_copsA1
volunteer_copsB1
good_security
unacquaintedB2
poor_security
B3foreign_cops
unacquaintedB2
poor_security
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Active Arg. Structure
S is active wrt. E iff S is well-formed, pr(S) $ E and &A ! args(S) is coherent
If S is active then &A ! args(S) is active
A is active iff 'S s.t. top(S) = A and S is active
(Minimality) If S is active then ∄Si ⋤ S s.t. Si is active
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Active Arg. Structure, e.g.
cA
d
a bB
cA
d
S1 S2
well-formed
arguments
are activeE = {a, b}
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Active Instance
F = ⟨E,W,⋈,pref⟩, the active instance is (S,R)
S: set of active arg. structures
R: active attack relation over S
The active instance of a DAF is a Dung’s AF
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Active Instance, e.g.
mcA2
gs
th psA3
dr
upcA1 vc
B1
gs
unB2
ps
B3fc
unB2
ps
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Active Instance, e.g.
mcA2
gs
th psA3
dr
upcA1 vc
B1
gs
unB2
ps
B3fc
unB2
ps
E1 = {mc, upc, th}
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Active Instance, e.g.
mcA2
gs
th psA3
dr
upcA1 vc
B1
gs
unB2
ps
B3fc
unB2
ps
E1 = {mc, upc, th}E2 = {mc, upc, th, vc}
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Active Instance, e.g.
mcA2
gs
th psA3
dr
upcA1 vc
B1
gs
unB2
ps
B3fc
unB2
ps
E2 = {mc, upc, th, vc}E3 = {upc, th, vc, un, fc}
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Active Instance, e.g.
mcA2
gs
th psA3
dr
upcA1 vc
B1
gs
unB2
ps
B3fc
unB2
ps
E3 = {upc, th, vc, un, fc} E4 = {upc, th, vc, fc}
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Changing the DAF
Evidence changes
Old arguments no longer reasonable
New arguments can be taken into account
Non-syntactic conflicts can be added/deleted
...any combination of the above
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Argument Contraction, e.g.
mcA2
gs
th psA3
dr
upcA1 vc
B1
gs
unB2
ps
B3fc
unB2
ps
E4 = {upc, th, vc, fc}
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Argument Contraction, e.g.
mcA2
gs
th psA3
dr
upcA1 vc
B1
gsunB2
ps
E4 = {upc, th, vc, fc}
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Semantics
Plenty of argumentation semantics have been defined over Dung’s AF
These results can be reutilised for the DAF through its active instance
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Conclusions
Richer representation for arguments
Consideration of argumental structures
Evidence as a separate entity
Active/Inactive knowledge
Change operations and dynamics
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Related/Future Work
Boella et al. approach on dynamics: framework changes that do not affect extensions
Our focus is KR; both approaches are combinable
Using the DAF for hypothetical/abductive reasoning
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Thank you
Questions?