Artificial Intelligence Presentation

1. Artificial Intelligence Presentation Chapter 7 – Logical Agents Jesse Brandao

2. Overview • What are Logical Agents • Knowledge Base • Logical Reasoning • Conclusion • Questions and Answers Session

3. Logical Agents General-purpose are knowledge agents with the following characteristics: • Combine the available information with their general knowledge • Use natural language • Reuse knowledge for novel tasks and can improve old tasks with new knowledge

4. Knowledge Base Agents have as a central component a Knowledge Base (KB), which is itself composed of a set of sentences in knowledge representation language (KRL)

5. Knowledge Base To manipulate its’ set of sentences it uses 3 main functions: • Tell: Add information from KB • Ask: Retrieve information from KB • Infer: Generate new sentences from existing ones

6. Knowledge Base Sentence in the knowledge base need to have 2 things: • Syntax, defines admissible sentences • Semantics, which define the truth of sentences

7. Logical Reasoning Logical reasoning requires Entailment, that is to say: From statement a, follows statement b

8. Inference Algorithms Sound algorithms: • Infers only entailed sentences • Truth preserving Complete algorithms: • Can derived any sentence which is entailed

9. Propositional Logic

10. Atomic Sentences • Consist of a single propositional symbol and function as mnemonics • Use upper case letters for representation • “True” is the always true proposition • “False” is the always false proposition

11. Complex Sentences Constructed with symbols via connectives: • ^ - Conjunctive symbol (And) • V - Disjunctive symbol (Or) • ~ - Negation symbol (Not) • => - Unidirectional implication symbol (Implies) •  - Bidirectional implication symbol (Iff)

12. Truth Tables

13. Entailment Concepts • Equivalence • Tautology • Satisfiability

14. Inference Rules Modus Ponens: • Sentence 1: A => B • Sentence 2: A • Inference: B

15. Inference Rules And-Elimination: • Setence 1: A ^ B • Inference: A • Inference: B

16. Proof Construction Like a search in that traverse a path of inference rules. Problem! How to ignore the countless irrelevant propositions? A good proof method ought to do just that.

17. Monotonicity Knowledge bases do not decrease because if: KB -> A then KB ^ B -> A, where B is a new sentence added to KB

18. Resolution Rule In disjunctive statements, the complementary sentences resolve each other and therefore one can infer the disjunction of the remaining non-complementary sentences

19. Resolution and Completeness The Resolution Rule is a complete inference method in that, in conjunction with any complete search method it can derive any entailment from the KB. However, it is a refutation completeness: • Can confirm any entailment from the KB • Unable to enumerate all entailments from the KB

20. Conjunctive Normal Form The resolution rule on works for disjunctions (V) with negations (~), but any  , => and ^ can be transformed in to a conjunctions of disjunctive clauses

21. Conjunctive Normal Form Eliminate  by biconditional elimination: • A  B = (A => B) ^ (B => A)

22. Conjunctive Normal Form Eliminate => by implication elimination: • (A => B) = ~A V B

23. Conjunctive Normal Form Eliminate external ~ by De Morgan’s law: • ~ (A ^ B) = (~A V ~B)

24. Resolution Algorithm

25. Horn Clauses Clause of disjunctive symbols with at most one positive The clauses can be written as an implication which allows for an easy inference by forward or back chaining Entailment can be determined with in a time linearly proportional to the size of KB

26. Horn Clauses Example: (~A V B V ~C) , which can be seen as (~[A ^ C] V B), by implication elimination, you get (A ^ C) => B

27. Conclusion

28. Questions and Answers