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Lecture 11

Lecture 11. More Propositional and Predicate Logic. Wednesday, 17 September 2003 William H. Hsu Department of Computing and Information Sciences, KSU http://www.kddresearch.org http://www.cis.ksu.edu/~bhsu Reading: Sections 6.1 – 6.4, Russell and Norvig. Lecture Outline. Today’s Reading

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Lecture 11

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  1. Lecture 11 More Propositional and Predicate Logic Wednesday, 17 September 2003 William H. Hsu Department of Computing and Information Sciences, KSU http://www.kddresearch.org http://www.cis.ksu.edu/~bhsu Reading: Sections 6.1 – 6.4, Russell and Norvig

  2. Lecture Outline • Today’s Reading • Sections 6.5 – 6.6, 7.1 – 7.3, Russell and Norvig • Recommended references: Nilsson and Genesereth • Previously: Logical Agents • Knowledge Bases (KB) and KB agents • Motivating example: Wumpus World • Logic in general • Syntax of propositional calculus • Today • Propositional calculus (concluded) • Normal forms • Production systems • Predicate logic • Introduction to First-Order Logic (FOL): examples, inference rules (sketch) • Next Week: First-Order Logic Review, Resolution Theorem Proving

  3. Turn to A Partner Exercise:Continuation Adapted from slides by S. Russell, UC Berkeley

  4. Review: Knowledge Representation (KR) forIntelligent Agent Problems • Percepts • What can agent observe? • What can sensors tell it? • Actions • What actuators does agent have? • In what context are they applicable? • Goals • What are agents goals? Preferences (utilities)? • How does agent evaluate them (check environment, deliberate, etc.)? • Environment • What are “rules of the world”? • How can these be represented, simulated?

  5. Review:Simple Knowledge-Based Agent Figure 6.1 p. 152 R&N Adapted from slides by S. Russell, UC Berkeley

  6. Review:Types of Logic Figure 6.7 p. 166 R&N Adapted from slides by S. Russell, UC Berkeley

  7. Propositional Logic: Semantics Adapted from slides by S. Russell, UC Berkeley

  8. Propositional Inference:Enumeration (Model Checking) Method Adapted from slides by S. Russell, UC Berkeley

  9. Normal Forms:CNF, DNF, Horn Adapted from slides by S. Russell, UC Berkeley

  10. Validity and Satisfiability Adapted from slides by S. Russell, UC Berkeley

  11. Proof Methods Adapted from slides by S. Russell, UC Berkeley

  12. Inference (Sequent) Rules forPropositional Logic Adapted from slides by S. Russell, UC Berkeley

  13. Logical Agents:Taking Stock Adapted from slides by S. Russell, UC Berkeley

  14. The Road Ahead:Predicate Logic and FOL • Predicate Logic • Enriching language • Predicates • Functions • Syntax and semantics of predicate logic • First-Order Logic (FOL, FOPC) • Need for quantifiers • Relation to (unquantified) predicate logic • Syntax and semantics of FOL • Fun with Sentences • Wumpus World in FOL Adapted from slides by S. Russell, UC Berkeley

  15. Syntax of FOL:Basic Elements Adapted from slides by S. Russell, UC Berkeley

  16. FOL: Atomic Sentences(Atomic Well-Formed Formulae) Adapted from slides by S. Russell, UC Berkeley

  17. Summary Points • Logical Agents Overview (Last Time) • Knowledge Bases (KB) and KB agents • Motivating example: Wumpus World • Logic in general • Syntax of propositional calculus • Propositional and First-Order Calculi (Today) • Propositional calculus (concluded) • Normal forms • Inference (aka sequent) rules • Production systems • Predicate logic without quantifiers • Introduction to First-Order Logic (FOL) • Examples • Inference rules (sketch) • Next Week: First-Order Logic Review, Intro to Resolution Theorem Proving

  18. Turn To A Partner Exercise [1]

  19. Turn To A Partner Exercise [2]

  20. Terminology • Logical Frameworks • Knowledge Bases (KB) • Logic in general: representation languages, syntax, semantics • Propositional logic • First-order logic (FOL, FOPC) • Model theory, domain theory: possible worlds semantics, entailment • Normal Forms • Conjunctive Normal Form (CNF) • Disjunctive Normal Form (DNF) • Horn Form • Proof Theory and Inference Systems • Sequent calculi: rules of proof theory • Derivability or provability • Properties • Soundness (derivability implies entailment) • Completeness (entailment implies derivability)

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