Docsity
Docsity

Prepare for your exams
Prepare for your exams

Study with the several resources on Docsity


Earn points to download
Earn points to download

Earn points by helping other students or get them with a premium plan


Guidelines and tips
Guidelines and tips

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

Some concept of Artificial Intelligence are Agents and Problem Solving, Autonomy, Programs, Classical and Modern Planning, First-Order Logic, Resolution Theorem Proving, Search Strategies, Structure Learning. Main points of this lecture are: First-Order Logic Two, Logical Agents, Calculi, Logical Agent Framework, Logic In General, Knowledge Representation, Inference, Theorem, Planning, Normal Forms

Typology: Slides

2012/2013

Uploaded on 04/29/2013

shantii
shantii 🇮🇳

4.4

(14)

98 documents

1 / 24

Toggle sidebar

This page cannot be seen from the preview

Don't miss anything!

bg1
Lecture 14 of 41
First-Order Logic
and Theorem Proving
Docsity.com
pf3
pf4
pf5
pf8
pf9
pfa
pfd
pfe
pff
pf12
pf13
pf14
pf15
pf16
pf17
pf18

Partial preview of the text

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

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