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

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Lecture 11 of 41

Intro to Propositional and Predicate Logic

Lecture Outline

• Today’s Reading
• 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

Review:

Simple Knowledge-Based Agent

Figure 6.1 p. 152 R&N

Review:

Types of Logic

Figure 6.7 p. 166 R&N

Propositional Inference:

Enumeration (Model Checking) Method

Normal Forms:

CNF, DNF, Horn

Proof Methods

Inference (Sequent) Rules for

Propositional Logic

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

Syntax of FOL:

Basic Elements

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

Fun with Sentences:

Family Feud

Adapted from slides by S. Russell, UC Berkeley

• Brothers are Siblings
  • ∀ x , y. Brother ( x , y ) ⇔ Sibling ( x , y )
• Siblings (i.e., Sibling Relationships) are Reflexive
  • ∀ x , y. Sibling ( x , y ) ⇔ Sibling ( y , x )
• One’s Mother is One’s Female Parent
  • ∀ x , y. Mother ( x , y ) ⇔ Female ( x ) ∧ Parent ( x , y )
• A First Cousin Is A Child of A Parent’s Sibling
  • ∀ x , y. First-Cousin ( x , y ) ⇔ ∃ p , ps. Parent ( p , x ) ∧ Sibling ( p , ps ) ∧ Parent ( ps , y )

Jigsaw Exercise [2]:

First-Order Logic Sentences

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)