Lecture 4: Logic

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Lecture 4: Logic

Logic & AI

Why Study Logic?

Logic, AI, and the Future of Mathematics

Symbolic vs. Connectionist AI

Two Paradigms

The Future: Neurosymbolic AI

Basics of Logic

Arguments

Validity

Soundness

Entailment

Propositional Logic

Vocabulary

Syntax Rules

Examples

Sentences and Semantics

Interpretation

Semantics

Model

Evaluating Sentences

Truth Tables

Important Notes on Implication

Satisfiability

Knowledge Bases

Definition

Model of a Knowledge Base

Entailment

Definition

Methods of Inference

Goal of Inference

Challenges

Inference Method 1: Enumeration

Model Checking

Inference Method 2: Using Logical Rules

Common Inference Rules

Logical Equivalences

Inference Method 3: Resolution

Conjunctive Normal Form (CNF)

Resolution Rule

Resolution Algorithm

First-Order Logic (FOL)

Limitations of Propositional Logic

FOL is More Expressive

FOL Syntax: Terms

Definition

Types of Terms

Ground Terms

FOL Syntax: Atoms and Predicates

Atoms

Predicates

Equality

FOL Syntax: Sentences

Sentence Types

Interpretation

FOL Quantifiers

Universal Quantifier: \forall

Example: All Humans Are Mammals

Existential Quantifier: \exists

Example: Some Humans Are Male

Practice Problems

Key Takeaways

Coming Up

Further Reading