Assertional Logickw.fudan.edu.cn/resources/ppt/invitedtalk/assertional... · 2017. 11. 21. ·...
Transcript of Assertional Logickw.fudan.edu.cn/resources/ppt/invitedtalk/assertional... · 2017. 11. 21. ·...
![Page 2: Assertional Logickw.fudan.edu.cn/resources/ppt/invitedtalk/assertional... · 2017. 11. 21. · still has problems, e.g., the frame problem, the ramification problem not that expressive](https://reader035.fdocuments.us/reader035/viewer/2022062403/5fd5df9047a4045316427702/html5/thumbnails/2.jpg)
2
Content • Motivation • Syntax and semantics • Extensions by definition • Incorporating FOL, probability and time • AL vs FOL • Potential applications • Conclusion
![Page 3: Assertional Logickw.fudan.edu.cn/resources/ppt/invitedtalk/assertional... · 2017. 11. 21. · still has problems, e.g., the frame problem, the ramification problem not that expressive](https://reader035.fdocuments.us/reader035/viewer/2022062403/5fd5df9047a4045316427702/html5/thumbnails/3.jpg)
3
Content • Motivation • Syntax and semantics • Extensions by definition • Incorporating FOL, probability and time • AL vs FOL • Potential applications • Conclusion
![Page 4: Assertional Logickw.fudan.edu.cn/resources/ppt/invitedtalk/assertional... · 2017. 11. 21. · still has problems, e.g., the frame problem, the ramification problem not that expressive](https://reader035.fdocuments.us/reader035/viewer/2022062403/5fd5df9047a4045316427702/html5/thumbnails/4.jpg)
Symbolic AI
P Q P∧Q P⋁Q PQ
T T T T T
T F F T F
F T F T T
F F F F T
![Page 5: Assertional Logickw.fudan.edu.cn/resources/ppt/invitedtalk/assertional... · 2017. 11. 21. · still has problems, e.g., the frame problem, the ramification problem not that expressive](https://reader035.fdocuments.us/reader035/viewer/2022062403/5fd5df9047a4045316427702/html5/thumbnails/5.jpg)
![Page 6: Assertional Logickw.fudan.edu.cn/resources/ppt/invitedtalk/assertional... · 2017. 11. 21. · still has problems, e.g., the frame problem, the ramification problem not that expressive](https://reader035.fdocuments.us/reader035/viewer/2022062403/5fd5df9047a4045316427702/html5/thumbnails/6.jpg)
6
But …
![Page 7: Assertional Logickw.fudan.edu.cn/resources/ppt/invitedtalk/assertional... · 2017. 11. 21. · still has problems, e.g., the frame problem, the ramification problem not that expressive](https://reader035.fdocuments.us/reader035/viewer/2022062403/5fd5df9047a4045316427702/html5/thumbnails/7.jpg)
Representation
Problem: one more building block, much more effort Challenge: how to make them living happily ever after
Proposition
Relation
Quantifier Rule
Probability Action
Time/Space Plan
Muliagents
Arithmetic
Preference Algorithm
Type Utility Modality Fuzzy
![Page 8: Assertional Logickw.fudan.edu.cn/resources/ppt/invitedtalk/assertional... · 2017. 11. 21. · still has problems, e.g., the frame problem, the ramification problem not that expressive](https://reader035.fdocuments.us/reader035/viewer/2022062403/5fd5df9047a4045316427702/html5/thumbnails/8.jpg)
Reasoning
Problem: more expressive less efficient, more efficient less expressive Challenge: both are needed but there is no free lunch
Expressiveness Efficiency
![Page 9: Assertional Logickw.fudan.edu.cn/resources/ppt/invitedtalk/assertional... · 2017. 11. 21. · still has problems, e.g., the frame problem, the ramification problem not that expressive](https://reader035.fdocuments.us/reader035/viewer/2022062403/5fd5df9047a4045316427702/html5/thumbnails/9.jpg)
Learning
Problem: KR reasoners are algorithm based, little power to learn Challenge: learnable reasoning
![Page 10: Assertional Logickw.fudan.edu.cn/resources/ppt/invitedtalk/assertional... · 2017. 11. 21. · still has problems, e.g., the frame problem, the ramification problem not that expressive](https://reader035.fdocuments.us/reader035/viewer/2022062403/5fd5df9047a4045316427702/html5/thumbnails/10.jpg)
6E: What we need
Elegant Extensible Expressive Efficient Educable Evolvable
representation
reasoning learning
AI
![Page 11: Assertional Logickw.fudan.edu.cn/resources/ppt/invitedtalk/assertional... · 2017. 11. 21. · still has problems, e.g., the frame problem, the ramification problem not that expressive](https://reader035.fdocuments.us/reader035/viewer/2022062403/5fd5df9047a4045316427702/html5/thumbnails/11.jpg)
Representation – a case study Situation calculus (FOL + action) ∀a,v,w,s: affects(a, on(v,w), s) → ∃x,y: a=move(v,x,y) ∀a,v,s: affects(a, clear(v), s) → (∃x,z: a=move(x,v,z)) ⋁ (∃x,y: a=move(x,y,v)) ∀a,v,w,s: affects(a, colour(v,w), s) → ∃x: a=paint(v,x)
Advantages clear, no ambiguity doable, e.g., Golog Issues needs to define a completely new syntax and semantics too complicate - no outsider can understand it still has problems, e.g., the frame problem, the ramification problem not that expressive – cannot quantifier over predicates, formulas not efficient at all too many more building blocks to be incorporated, e.g., plan, probability, time.
![Page 12: Assertional Logickw.fudan.edu.cn/resources/ppt/invitedtalk/assertional... · 2017. 11. 21. · still has problems, e.g., the frame problem, the ramification problem not that expressive](https://reader035.fdocuments.us/reader035/viewer/2022062403/5fd5df9047a4045316427702/html5/thumbnails/12.jpg)
Representation
Problem: one more building block, much more effort Challenge: how to make them living happily ever after
Proposition
Relation
Quantifier Rule
Probability Action
Time/Space Plan
Muliagents
Arithmetic
Preference Algorithm
Type Utility Modality Fuzzy
Solution: assertional logic
Elegant Extensible Expressive
![Page 13: Assertional Logickw.fudan.edu.cn/resources/ppt/invitedtalk/assertional... · 2017. 11. 21. · still has problems, e.g., the frame problem, the ramification problem not that expressive](https://reader035.fdocuments.us/reader035/viewer/2022062403/5fd5df9047a4045316427702/html5/thumbnails/13.jpg)
13
Content • Motivation • Syntax and semantics • Extensions by definition • Incorporating FOL, probability and time • AL vs FOL • Potential applications • Conclusion
![Page 14: Assertional Logickw.fudan.edu.cn/resources/ppt/invitedtalk/assertional... · 2017. 11. 21. · still has problems, e.g., the frame problem, the ramification problem not that expressive](https://reader035.fdocuments.us/reader035/viewer/2022062403/5fd5df9047a4045316427702/html5/thumbnails/14.jpg)
Assertional Logic
Formalization
Knowledge
Individual Concept Operator
Element Set Function a=b
x or O(x1,…,xn) I(a)=I(b)
Syntax Semantics
![Page 15: Assertional Logickw.fudan.edu.cn/resources/ppt/invitedtalk/assertional... · 2017. 11. 21. · still has problems, e.g., the frame problem, the ramification problem not that expressive](https://reader035.fdocuments.us/reader035/viewer/2022062403/5fd5df9047a4045316427702/html5/thumbnails/15.jpg)
15
Content • Motivation • Syntax and semantics • Extensions by definition • Incorporating FOL, probability and time • AL vs FOL • Potential applications • Conclusion
![Page 16: Assertional Logickw.fudan.edu.cn/resources/ppt/invitedtalk/assertional... · 2017. 11. 21. · still has problems, e.g., the frame problem, the ramification problem not that expressive](https://reader035.fdocuments.us/reader035/viewer/2022062403/5fd5df9047a4045316427702/html5/thumbnails/16.jpg)
Definition - Individual
i=a
1=Succ(0)
![Page 17: Assertional Logickw.fudan.edu.cn/resources/ppt/invitedtalk/assertional... · 2017. 11. 21. · still has problems, e.g., the frame problem, the ramification problem not that expressive](https://reader035.fdocuments.us/reader035/viewer/2022062403/5fd5df9047a4045316427702/html5/thumbnails/17.jpg)
Definition - Operator
Op(C1,…,Cn)=T(C1,…,Cn)
Succ(n)={n,{n}} Uncle(x)=Brother(Father(x))
![Page 18: Assertional Logickw.fudan.edu.cn/resources/ppt/invitedtalk/assertional... · 2017. 11. 21. · still has problems, e.g., the frame problem, the ramification problem not that expressive](https://reader035.fdocuments.us/reader035/viewer/2022062403/5fd5df9047a4045316427702/html5/thumbnails/18.jpg)
Definition - Concept Enumeration C={i1,…,in} Digit={1,2…,9} Operation C=C1∩C2 Man=Human∩Male
Replacement C’=Op(C) Parent=ParentOf(Human)
Comprehension C’=C|A(C) Male=Animal|Sex(Animal)=Male
![Page 19: Assertional Logickw.fudan.edu.cn/resources/ppt/invitedtalk/assertional... · 2017. 11. 21. · still has problems, e.g., the frame problem, the ramification problem not that expressive](https://reader035.fdocuments.us/reader035/viewer/2022062403/5fd5df9047a4045316427702/html5/thumbnails/19.jpg)
Multi-Assertions
M-A::=
Mn(a1=b1,…,an=bn)::=(a1,…,an)=(b1,…,bn)
![Page 20: Assertional Logickw.fudan.edu.cn/resources/ppt/invitedtalk/assertional... · 2017. 11. 21. · still has problems, e.g., the frame problem, the ramification problem not that expressive](https://reader035.fdocuments.us/reader035/viewer/2022062403/5fd5df9047a4045316427702/html5/thumbnails/20.jpg)
Nested Assertions
![Page 21: Assertional Logickw.fudan.edu.cn/resources/ppt/invitedtalk/assertional... · 2017. 11. 21. · still has problems, e.g., the frame problem, the ramification problem not that expressive](https://reader035.fdocuments.us/reader035/viewer/2022062403/5fd5df9047a4045316427702/html5/thumbnails/21.jpg)
21
Content • Motivation • Syntax and semantics • Extensions by definition • Incorporating FOL, probability and time • AL vs FOL • Potential applications • Conclusion
![Page 22: Assertional Logickw.fudan.edu.cn/resources/ppt/invitedtalk/assertional... · 2017. 11. 21. · still has problems, e.g., the frame problem, the ramification problem not that expressive](https://reader035.fdocuments.us/reader035/viewer/2022062403/5fd5df9047a4045316427702/html5/thumbnails/22.jpg)
Propositional Connectives
![Page 23: Assertional Logickw.fudan.edu.cn/resources/ppt/invitedtalk/assertional... · 2017. 11. 21. · still has problems, e.g., the frame problem, the ramification problem not that expressive](https://reader035.fdocuments.us/reader035/viewer/2022062403/5fd5df9047a4045316427702/html5/thumbnails/23.jpg)
Quantifiers
![Page 24: Assertional Logickw.fudan.edu.cn/resources/ppt/invitedtalk/assertional... · 2017. 11. 21. · still has problems, e.g., the frame problem, the ramification problem not that expressive](https://reader035.fdocuments.us/reader035/viewer/2022062403/5fd5df9047a4045316427702/html5/thumbnails/24.jpg)
(Conditional) Probability
![Page 25: Assertional Logickw.fudan.edu.cn/resources/ppt/invitedtalk/assertional... · 2017. 11. 21. · still has problems, e.g., the frame problem, the ramification problem not that expressive](https://reader035.fdocuments.us/reader035/viewer/2022062403/5fd5df9047a4045316427702/html5/thumbnails/25.jpg)
Time (Point)
![Page 26: Assertional Logickw.fudan.edu.cn/resources/ppt/invitedtalk/assertional... · 2017. 11. 21. · still has problems, e.g., the frame problem, the ramification problem not that expressive](https://reader035.fdocuments.us/reader035/viewer/2022062403/5fd5df9047a4045316427702/html5/thumbnails/26.jpg)
26
Content • Motivation • Syntax and semantics • Extensions by definition • Incorporating FOL, probability and time • AL vs FOL • Potential applications • Conclusion
![Page 27: Assertional Logickw.fudan.edu.cn/resources/ppt/invitedtalk/assertional... · 2017. 11. 21. · still has problems, e.g., the frame problem, the ramification problem not that expressive](https://reader035.fdocuments.us/reader035/viewer/2022062403/5fd5df9047a4045316427702/html5/thumbnails/27.jpg)
AL vs High-Order Logic
C Concept of HOL Same individuals FOL
Different individuals Many sorted FOL Concepts Monadic SOL Operators SOL
Operators of … operators HOL
Assertions ???
Elegant Expressive Extensible
![Page 28: Assertional Logickw.fudan.edu.cn/resources/ppt/invitedtalk/assertional... · 2017. 11. 21. · still has problems, e.g., the frame problem, the ramification problem not that expressive](https://reader035.fdocuments.us/reader035/viewer/2022062403/5fd5df9047a4045316427702/html5/thumbnails/28.jpg)
AL for knowledge representation Advantages clear, no ambiguity ✔ doable ✔ Issues needs to define a completely new syntax and semantics ✖ too complicated - no outsider can understand it ✖ not that expressive ✖ too many more building blocks to be incorporated extensible not efficient at all TBA
![Page 29: Assertional Logickw.fudan.edu.cn/resources/ppt/invitedtalk/assertional... · 2017. 11. 21. · still has problems, e.g., the frame problem, the ramification problem not that expressive](https://reader035.fdocuments.us/reader035/viewer/2022062403/5fd5df9047a4045316427702/html5/thumbnails/29.jpg)
AL vs Description Logic I
![Page 30: Assertional Logickw.fudan.edu.cn/resources/ppt/invitedtalk/assertional... · 2017. 11. 21. · still has problems, e.g., the frame problem, the ramification problem not that expressive](https://reader035.fdocuments.us/reader035/viewer/2022062403/5fd5df9047a4045316427702/html5/thumbnails/30.jpg)
AL vs Description Logic II AL Description Logic
n-ary operators Binary relations Comprehension/Replacement Role Restriction
Complex assertions/quantifiers Fragment of FOL a=b Different kinds
Extensibility by definition Extensibility by new components
![Page 31: Assertional Logickw.fudan.edu.cn/resources/ppt/invitedtalk/assertional... · 2017. 11. 21. · still has problems, e.g., the frame problem, the ramification problem not that expressive](https://reader035.fdocuments.us/reader035/viewer/2022062403/5fd5df9047a4045316427702/html5/thumbnails/31.jpg)
31
Content • Motivation • Syntax and semantics • Extensions by definition • Incorporating FOL, probability and time • AL vs FOL • Potential applications • Conclusion
![Page 32: Assertional Logickw.fudan.edu.cn/resources/ppt/invitedtalk/assertional... · 2017. 11. 21. · still has problems, e.g., the frame problem, the ramification problem not that expressive](https://reader035.fdocuments.us/reader035/viewer/2022062403/5fd5df9047a4045316427702/html5/thumbnails/32.jpg)
Mathematics test
![Page 33: Assertional Logickw.fudan.edu.cn/resources/ppt/invitedtalk/assertional... · 2017. 11. 21. · still has problems, e.g., the frame problem, the ramification problem not that expressive](https://reader035.fdocuments.us/reader035/viewer/2022062403/5fd5df9047a4045316427702/html5/thumbnails/33.jpg)
Natural language formalization
Noun: Concept Adjective: unary Boolean operator
![Page 34: Assertional Logickw.fudan.edu.cn/resources/ppt/invitedtalk/assertional... · 2017. 11. 21. · still has problems, e.g., the frame problem, the ramification problem not that expressive](https://reader035.fdocuments.us/reader035/viewer/2022062403/5fd5df9047a4045316427702/html5/thumbnails/34.jpg)
From database to knowledge base
![Page 35: Assertional Logickw.fudan.edu.cn/resources/ppt/invitedtalk/assertional... · 2017. 11. 21. · still has problems, e.g., the frame problem, the ramification problem not that expressive](https://reader035.fdocuments.us/reader035/viewer/2022062403/5fd5df9047a4045316427702/html5/thumbnails/35.jpg)
35
Content • Motivation • Syntax and semantics • Extensions by definition • Incorporating FOL, probability and time • AL vs FOL • Potential applications • Conclusion
![Page 36: Assertional Logickw.fudan.edu.cn/resources/ppt/invitedtalk/assertional... · 2017. 11. 21. · still has problems, e.g., the frame problem, the ramification problem not that expressive](https://reader035.fdocuments.us/reader035/viewer/2022062403/5fd5df9047a4045316427702/html5/thumbnails/36.jpg)
36
Concluding Remarks Knowledge representation: from FOL to AL Why FOL is not perfect? Elegancy, Extensibility and Expressivity AL – syntax and semantics AL – extensibility via definitions Why AL is better than FOL?
![Page 37: Assertional Logickw.fudan.edu.cn/resources/ppt/invitedtalk/assertional... · 2017. 11. 21. · still has problems, e.g., the frame problem, the ramification problem not that expressive](https://reader035.fdocuments.us/reader035/viewer/2022062403/5fd5df9047a4045316427702/html5/thumbnails/37.jpg)
37
More on AL representation actions and their effects plans, method and hints incomplete information and null
![Page 38: Assertional Logickw.fudan.edu.cn/resources/ppt/invitedtalk/assertional... · 2017. 11. 21. · still has problems, e.g., the frame problem, the ramification problem not that expressive](https://reader035.fdocuments.us/reader035/viewer/2022062403/5fd5df9047a4045316427702/html5/thumbnails/38.jpg)
Reasoning
Problem: more expressive less efficient, more efficient less expressive Challenge: both are needed but there is no free lunch
Expressiveness Efficiency
Solution: reasoning by knowledge
Efficient
![Page 39: Assertional Logickw.fudan.edu.cn/resources/ppt/invitedtalk/assertional... · 2017. 11. 21. · still has problems, e.g., the frame problem, the ramification problem not that expressive](https://reader035.fdocuments.us/reader035/viewer/2022062403/5fd5df9047a4045316427702/html5/thumbnails/39.jpg)
Learning
Problem: KR reasoners are algorithm based, little power to learn Challenge: learnable reasoning
Educable Evolvable
Solution: learnable knowledge
![Page 40: Assertional Logickw.fudan.edu.cn/resources/ppt/invitedtalk/assertional... · 2017. 11. 21. · still has problems, e.g., the frame problem, the ramification problem not that expressive](https://reader035.fdocuments.us/reader035/viewer/2022062403/5fd5df9047a4045316427702/html5/thumbnails/40.jpg)
Thank you!