Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Lecture 13 of 41 More Propositional and Predicate Logic 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 CIS 730: Introduction to Artificial Intelligence Kansas State University Department of Computing and Information Sciences 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 CIS 730: Introduction to Artificial Intelligence Kansas State University Department of Computing and Information Sciences Validity and Satisfiability Adapted from slides by S. Russell, UC Berkeley CIS 730: Introduction to Artificial Intelligence Kansas State University Department of Computing and Information Sciences Proof Methods Adapted from slides by S. Russell, UC Berkeley CIS 730: Introduction to Artificial Intelligence Kansas State University Department of Computing and Information Sciences Logical Agents: Taking Stock Adapted from slides by S. Russell, UC Berkeley CIS 730: Introduction to Artificial Intelligence Kansas State University Department of Computing and Information Sciences FOL: Atomic Sentences (Atomic Well-Formed Formulae) Adapted from slides by S. Russell, UC Berkeley CIS 730: Introduction to Artificial Intelligence Kansas State University Department of Computing and Information Sciences FOL: Complex Sentences (Well-Formed Formulae) Adapted from slides by S. Russell, UC Berkeley CIS 730: Introduction to Artificial Intelligence Kansas State University Department of Computing and Information Sciences Truth in FOL Adapted from slides by S. Russell, UC Berkeley CIS 730: Introduction to Artificial Intelligence Kansas State University Department of Computing and Information Sciences Models for FOL: Example Adapted from slides by S. Russell, UC Berkeley CIS 730: Introduction to Artificial Intelligence Kansas State University Department of Computing and Information Sciences Universal Quantification Adapted from slides by S. Russell, UC Berkeley CIS 730: Introduction to Artificial Intelligence Kansas State University Department of Computing and Information Sciences Existential Quantification Adapted from slides by S. Russell, UC Berkeley CIS 730: Introduction to Artificial Intelligence Kansas State University Department of Computing and Information Sciences Quantifier Properties Adapted from slides by S. Russell, UC Berkeley CIS 730: Introduction to Artificial Intelligence Kansas State University Department of Computing and Information Sciences 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 CIS 730: Introduction to Artificial Intelligence Kansas State University Department of Computing and Information Sciences Automated Deduction (Chapters 8-10 R&N) Adapted from slides by S. Russell, UC Berkeley CIS 730: Introduction to Artificial Intelligence Kansas State University Department of Computing and Information Sciences Example Proof • ??? • Apply Sequent Rules to Generate New Assertions • Modus Ponens And Introduction Universal Elimination Adapted from slides by S. Russell, UC Berkeley CIS 730: Introduction to Artificial Intelligence Kansas State University Department of Computing and Information Sciences Search with Primitive Inference Rules Adapted from slides by S. Russell, UC Berkeley CIS 730: Introduction to Artificial Intelligence Kansas State University Department of Computing and Information Sciences A Brief History of Reasoning: Chapter 8 End Notes, R&N Adapted from slides by S. Russell, UC Berkeley CIS 730: Introduction to Artificial Intelligence Kansas State University Department of Computing and Information Sciences 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 CIS 730: Introduction to Artificial Intelligence Kansas State University Department of Computing and Information Sciences 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/ • (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 CIS 730: Introduction to Artificial Intelligence Kansas State University Department of Computing and Information Sciences Unification: Definitions and Idea Sketch Adapted from slides by S. Russell, UC Berkeley CIS 730: Introduction to Artificial Intelligence Kansas State University Department of Computing and Information Sciences Generalized Modus Ponens Adapted from slides by S. Russell, UC Berkeley CIS 730: Introduction to Artificial Intelligence Kansas State University Department of Computing and Information Sciences Soundness of GMP Adapted from slides by S. Russell, UC Berkeley CIS 730: Introduction to Artificial Intelligence Kansas State University Department of Computing and Information Sciences 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 CIS 730: Introduction to Artificial Intelligence Kansas State University Department of Computing and Information Sciences 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…) CIS 730: Introduction to Artificial Intelligence Kansas State University Department of Computing and Information Sciences