1. Kansas State University Department of Computing and Information Sciences CIS 730: Introduction to Artificial Intelligence Lecture 14 of 42 Wednesday, 22 September 2004 William H. Hsu Department of Computing and Information Sciences, KSU http://www.kddresearch.org http://www.cis.ksu.edu/~bhsu Reading: Sections 8.1-8.3, Russell and Norvig 2e Review: Chapter 6, R&N 2e First-Order Logic 2 of 4: Theorem Proving

2. Kansas State University Department of Computing and Information Sciences CIS 730: Introduction to Artificial Intelligence Lecture Outline Today’s Reading –Chapter 8, Russell and Norvig –Recommended references: Nilsson and Genesereth (excerpt of Chapter 5 online) Next Week’s Reading: Chapters 9-10, R&N Previously: Introduction to Propositional and First-Order Logic –Last Friday (17 Sep 2004) FOL agents, issues: frame, ramification, qualification problems Solutions: situation calculus, circumscription by successor state axioms –Monday (20 Sep 2004) First-order logic (FOL): predicates, functions, quantifiers Sequent rules, proof by refutation Today: FOL Knowledge Bases and Theorem Proving –Forward Chaining with And-Introduction, Universal Elimination, Modus Ponens –Ontology, History of Logic, Russell’s Paradox –Unification, Logic Programming Basics Next Week: Resolution, Logic Programming, Decidability of SAT

3. Kansas State University Department of Computing and Information Sciences CIS 730: Introduction to Artificial Intelligence Adapted from slides by S. Russell, UC Berkeley Search with Primitive Inference Rules

4. Kansas State University Department of Computing and Information Sciences CIS 730: Introduction to Artificial Intelligence Adapted from slides by S. Russell, UC Berkeley Unification: Definitions and Idea Sketch

5. Kansas State University Department of Computing and Information Sciences CIS 730: Introduction to Artificial Intelligence Adapted from slides by S. Russell, UC Berkeley Generalized Modus Ponens

6. Kansas State University Department of Computing and Information Sciences CIS 730: Introduction to Artificial Intelligence Adapted from slides by S. Russell, UC Berkeley Soundness of GMP

7. Kansas State University Department of Computing and Information Sciences CIS 730: Introduction to Artificial Intelligence Adapted from slides by S. Russell, UC Berkeley Forward Chaining

8. Kansas State University Department of Computing and Information Sciences CIS 730: Introduction to Artificial Intelligence Adapted from slides by S. Russell, UC Berkeley Example: Forward Chaining

9. Kansas State University Department of Computing and Information Sciences CIS 730: Introduction to Artificial Intelligence Adapted from slides by S. Russell, UC Berkeley Backward Chaining

10. Kansas State University Department of Computing and Information Sciences CIS 730: Introduction to Artificial Intelligence Adapted from slides by S. Russell, UC Berkeley Example: Backward Chaining

11. Kansas State University Department of Computing and Information Sciences CIS 730: Introduction to Artificial Intelligence Question: How Does This Relate to Proof by Refutation? Answer –Suppose ¬Query, For The Sake Of Contradiction (FTSOC) –Attempt to prove that KB  ¬Query   Adapted from slides by S. Russell, UC Berkeley Review: Backward Chaining

12. Kansas State University Department of Computing and Information Sciences CIS 730: Introduction to Artificial Intelligence Adapted from slides by S. Russell, UC Berkeley Completeness Redux

13. Kansas State University Department of Computing and Information Sciences CIS 730: Introduction to Artificial Intelligence Adapted from slides by S. Russell, UC Berkeley Completeness in FOL

14. Kansas State University Department of Computing and Information Sciences CIS 730: Introduction to Artificial Intelligence Adapted from slides by S. Russell, UC Berkeley Resolution Inference Rule

15. Kansas State University Department of Computing and Information Sciences CIS 730: Introduction to Artificial Intelligence Adapted from slides by S. Russell, UC Berkeley Digression: Decidability and Formal Languages See: Hopcroft and Ullman 2e, Lewis and Papadimitriou 3e Formal Languages (See: CIS 540, Other Automata Theory Course) –Member of Turing hierarchy Finite state automata: regular languages Pushdown automata: context-free languages Linear bounded automata: context-sensitive languages Turing machines: recursive languages –Recursive languages  computational model for decision problem, halts in finite number of steps REC: set of all recursive languages Example: finite searches (convert to decision problem of checking solution) Closed under complementation (consequence?) –Recursive enumerable but not recursive (RE - REC) –Not recursive (  RE) What Are FOL-VALID, FOL-NOT-SAT, FOL-SAT, FOL-NOT-VALID?

16. Kansas State University Department of Computing and Information Sciences CIS 730: Introduction to Artificial Intelligence Knowledge Engineering KE: Process of –Choosing logical language (basis of KR) –Building KB –Implementing proof theory –Inferring new facts Analogy: Programming Languages / Software Engineering –Choosing programming language (basis of software engineering) –Writing program –Choosing / writing compiler –Running program Example Domains –Electronic circuits (Section 8.3 R&N) –Exercise Look up, read about protocol analysis Find example and think about KE process for your project domain

17. Kansas State University Department of Computing and Information Sciences CIS 730: Introduction to Artificial Intelligence Ontology Ontology: “What Objects Exist and Are Symbolically Representable?” Issue: Grouping Objects and Describing Families –Grouping objects and describing families –Example: sets of sets Russell’s paradox: http://plato.stanford.edu/entries/russell-paradox/http://plato.stanford.edu/entries/russell-paradox/ (Four) responses: types, formalism, intuitionism, Zermelo-Fraenkel set theory –Sidebar: natural kinds (p. 232) Issue: Reasoning About Time –Modal logics (CIS 301) –Interval logics (Section 8.4 R&N p. 238-241) Example Domains –Grocery shopping (Section 8.5 R&N); similar example in Winston 3e –Data models for knowledge discovery in databases (KDD) Data dictionaries See grocery example, especially p. 249 - 252

18. Kansas State University Department of Computing and Information Sciences CIS 730: Introduction to Artificial Intelligence Summary Points Applications of Knowledge Bases (KBs) and Inference Systems “Industrial Strength” KBs –Building KBs Knowledge Engineering (KE) and protocol analysis Inductive Logic Programming (ILP) and other machine learning techniques –Components Ontologies Fact and rule bases –Using KBs Systems of Sequent Rules: GMP/AI/UE, Resolution Methodology of Inference –Inference as search –Forward and backward chaining –Fan-in, fan-out

19. Kansas State University Department of Computing and Information Sciences CIS 730: Introduction to Artificial Intelligence Terminology Logical Languages: WFFs, Quantification Properties of Knowledge Bases (KBs) –Satisfiability and validity –Entailment and provability Properties of Proof Systems: Soundness and Completeness Knowledge Bases in Practice –Knowledge Engineering –Ontologies Sequent Rules –(Generalized) Modus Ponens –And-Introduction –Universal-Elimination Methodology of Inference –Forward and backward chaining –Fan-in, fan-out (wax on, wax off…)