First-Order Logic Two - Artificial Intelligence - Lecture Slides, Slides of Artificial Intelligence

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Lecture 14 of 41

First-Order Logic

and Theorem Proving

Lecture Outline

• Today’s Reading
• Next Week’s Reading: Chapters 9-10, R&N
• Previously: Introduction to Propositional and First-Order Logic
  • Last Friday (17 Sep 2004)
    • FOL agents, issues: frame, ramification, qualification problems
    • Solutions: situation calculus, circumscription by successor state axioms
  • Monday (20 Sep 2004)
    • First-order logic (FOL): predicates, functions, quantifiers
    • Sequent rules, proof by refutation
• Today: FOL Knowledge Bases and Theorem Proving
  • Forward Chaining with And-Introduction, Universal Elimination, Modus Ponens
  • Ontology, History of Logic, Russell’s Paradox
  • Unification, Logic Programming Basics
• Next Week: Resolution, Logic Programming, Decidability of SAT

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)

Search with Primitive Inference Rules

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

Unification:

Definitions and Idea Sketch

Soundness of GMP

Forward Chaining

Backward Chaining

Example:

Backward Chaining

Completeness Redux

Completeness in FOL