Propositional and Predicate Logic Two - Artificial Intelligence - Lecture Slides, Slides of Artificial Intelligence

Download Propositional and Predicate Logic Two - Artificial Intelligence - Lecture Slides and more Slides Artificial Intelligence in PDF only on Docsity!

Lecture 13 of 41

More Propositional and Predicate Logic

Lecture Outline

• Today’s Reading
• 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

Proof Methods

Logical Agents:

Taking Stock

FOL: Complex Sentences

(Well-Formed Formulae)

Truth in FOL

Universal Quantification

Existential Quantification

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

Automated Deduction (Chapters 8-10 R&N)

Adapted from slides by S. Russell, UC Berkeley

Adapted from slides by S. Russell, UC Berkeley

Search with Primitive Inference Rules

Adapted from slides by S. Russell, UC Berkeley

A Brief History of Reasoning:

Chapter 8 End Notes, R&N

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

Adapted from slides by S. Russell, UC Berkeley

Unification:

Definitions and Idea Sketch