Lecture 13 of 41. More Propositional and Predicate Logic

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1 Lecture 13 of 41 More Propositional and Predicate Logic Monday, 20 September 2004 William H. Hsu, KSU Reading: Sections , Russell and Norvig 2e Review: Chapter 6, R&N 2e

2 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 Validity and Satisfiability

4 Proof Methods

5 Logical Agents: Taking Stock

6 FOL: Atomic Sentences (Atomic Well-Formed Formulae)

7 FOL: Complex Sentences (Well-Formed Formulae)

8 Truth in FOL

9 Models for FOL: Example

10 Universal Quantification

11 Existential Quantification

12 Quantifier Properties

13 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 Automated Deduction (Chapters R&N)

15 Example Proof??? Apply Sequent Rules to Generate New Assertions Modus Ponens And Introduction Universal Elimination

16 Search with Primitive Inference Rules

17 A Brief History of Reasoning: Chapter 8 End Notes, R&N

18 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 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: (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 ) 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

20 Unification: Definitions and Idea Sketch

21 Generalized Modus Ponens

22 Soundness of GMP

23 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 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 )

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