Download presentation

Presentation is loading. Please wait.

Published byGeorgia Seeger Modified over 2 years ago

1
Auto-Epistemic Logic Proposed by Moore (1985) Contemplates reflection on self knowledge (auto-epistemic) Permits to talk not just about the external world, but also about the knowledge I have of it

2
Syntax of AEL 1st Order Logic, plus the operator L (applied to formulas) L signifies “I know ” Examples: place → L place (or L place → place) young (X) L studies (X) → studies (X)

3
Meaning of AEL What do I know? –What I can derive (in all models) And what do I know not? –What I cannot derive But what can be derived depends on what I know –Add knowledge, then test

4
Semantics of AEL T* is an expansion of theory T iff T* = Th(T { L : T* |= } { L : T* |≠ }) Assuming the inference rule / L : T* = Cn AEL (T { L : T* |≠ }) An AEL theory is always two-valued in L, that is, for every expansion: | L T* L T*

5
Knowledge vs. Belief Belief is a weaker concept –For every formula, I know it or know it not –There may be formulas I do not believe in, neither their contrary The Auto-Epistemic Logic of knowledge and belief (AELB), introduces also operator B – I believe in

6
AELB Example I rent a film if I believe I’m neither going to baseball nor football games B baseball B football → rent_filme I don’t buy tickets if I don’t know I’m going to baseball nor know I’m going to football L baseball L football → buy_tickets I’m going to football or baseball baseball football I should not conclude that I rent a film, but do conclude I should not buy tickets

7
Axioms about beliefs Consistency Axiom B Normality Axiom B (F → G) → ( B F → B G) Necessitation rule F B F

8
Minimal models In what do I believe? –In that which belongs to all preferred models Which are the preferred models? –Those that, for one same set of beliefs, have a minimal number of true things A model M is minimal iff there does not exist a smaller model N, coincident with M on B e L atoms When is true in all minimal models of T, we write T |= min

9
AELB expansions T* is a static expansion of T iff T* = Cn AELB (T { L : T* |≠ } { B : T* |= min }) where Cn AELB denotes closure using the axioms of AELB plus necessitation for L

10
The special case of AEB Because of its properties, the case of theories without the knowledge operator is especially interesting Then, the definition of expansion becomes: T* = (T*) where (T*) = Cn AEB (T { B : T* |= min }) and Cn AEB denotes closure using the axioms of AEB

11
Least expansion Theorem: Operator is monotonic, i.e. T T 1 T 2 → (T 1 ) (T 2 ) Hence, there always exists a minimal expansion of T, obtainable by transfinite induction: –T 0 = Cn (T) –T i+1 = (T i ) –T = U T (for limit ordinals )

12
Consequences Every AEB theory has at least one expansion If a theory is affirmative (i.e. all clauses have at least a positive literal) then it has at least a consistent expansion There is a procedure to compute the semantics

Similar presentations

Presentation is loading. Please wait....

OK

Restricted Satisfiability (SAT) Problem

Restricted Satisfiability (SAT) Problem

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on teachers day cards Ppt on network file system in linux Ppt on national education policy 1986 world Table manners for kids ppt on batteries Properties of matter for kids ppt on batteries Ppt on history of computer generations Ppt on digital image processing free download Ppt on automobile related topics about work Free download ppt on palm vein technology Ppt on central limit theorem proof