1. Kansas State University Department of Computing and Information Sciences CIS 730: Introduction to Artificial Intelligence Lecture 13 of 41 Monday, 20 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 More Propositional and Predicate Logic

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: Propositional and First-Order Logic –Last Wednesday (15 Sep 2004) Logical agent framework Logic in general: tools for KR, inference, problem solving Propositional logic: normal forms, sequent rules (modus ponens, resolution) First-order logic (FOL): predicates, functions, quantifiers –Last Friday (17 Sep 2004) FOL agents, issues: frame, ramification, qualification problems Solutions: situation calculus, circumscription by successor state axioms Today: FOL Knowledge Bases Next Week: Resolution Theorem Proving, Logic Programming Basics

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

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

5. Kansas State University Department of Computing and Information Sciences CIS 730: Introduction to Artificial Intelligence Adapted from slides by S. Russell, UC Berkeley Logical Agents: Taking Stock

6. Kansas State University Department of Computing and Information Sciences CIS 730: Introduction to Artificial Intelligence Adapted from slides by S. Russell, UC Berkeley FOL: Atomic Sentences (Atomic Well-Formed Formulae)

7. Kansas State University Department of Computing and Information Sciences CIS 730: Introduction to Artificial Intelligence Adapted from slides by S. Russell, UC Berkeley FOL: Complex Sentences (Well-Formed Formulae)

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

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

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

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

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

13. Kansas State University Department of Computing and Information Sciences CIS 730: Introduction to Artificial Intelligence Taking Stock: FOL Inference Previously: Logical Agents and Calculi Review: FOL in Practice –Agent “toy” world: Wumpus World in FOL –Situation calculus –Frame problem and variants (see R&N sidebar) Representational vs. inferential frame problems Qualification problem: “what if?” Ramification problem: “what else?” (side effects) –Successor-state axioms FOL Knowledge Bases FOL Inference –Proofs –Pattern-matching: unification –Theorem-proving as search Generalized Modus Ponens (GMP) Forward Chaining and Backward Chaining

14. Kansas State University Department of Computing and Information Sciences CIS 730: Introduction to Artificial Intelligence Automated Deduction (Chapters 8-10 R&N) Adapted from slides by S. Russell, UC Berkeley

15. Kansas State University Department of Computing and Information Sciences CIS 730: Introduction to Artificial Intelligence ??? Apply Sequent Rules to Generate New Assertions Modus Ponens And Introduction Universal Elimination Adapted from slides by S. Russell, UC Berkeley Example Proof

16. 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

17. Kansas State University Department of Computing and Information Sciences CIS 730: Introduction to Artificial Intelligence Adapted from slides by S. Russell, UC Berkeley A Brief History of Reasoning: Chapter 8 End Notes, R&N

18. 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

19. 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

20. 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

21. 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

22. 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

23. 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

24. 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…)