Unit 5 Overview: Introduction to Logic in AI

Unit 5: Introduction to Logic in AI — Overview

Connection to Unit 4: In Unit 4, you explored constraint satisfaction problems — situations where an agent must find an assignment that satisfies a set of rules simultaneously. Logic is the formal language that lets us write those rules precisely. This unit teaches you to read and write that language.

Learning Objectives

By the end of Unit 5, you will be able to:

  1. Explain why formal logic is necessary for AI knowledge representation

  2. Identify and eliminate ambiguity in natural language by translating statements into logical notation

  3. Construct and evaluate truth tables for propositional logic formulas

  4. Apply logical equivalence laws (De Morgan’s, distribution, double negation) to simplify formulas

  5. Trace the historical development of logic from Aristotle to modern AI systems

  6. Use universal and existential quantifiers to express general statements in first-order logic

  7. Recognize how logic underpins databases, circuit design, and AI planning systems

Reading Assignments

forall x: Calgary by P.D. Magnus, Tim Button, and Richard Zach (CC BY 4.0)

Chapters 1—​9 cover the complete propositional logic curriculum for this unit. Chapter 1 introduces the motivation for formal logic; Chapters 4—​6 cover connectives and truth tables; Chapters 7—​9 address equivalences and validity.

Berkeley CS 188: Logic and Knowledge Representation (CC BY-SA 4.0)

Sections on propositional logic, knowledge bases, and first-order logic connect this week’s material to the inference and reasoning systems in Unit 6.

Weekly Schedule

Section Topic Est. Time

5.0

Overview (this page)

10 min

5.1

Why Logic? From Natural Language to Formal Reasoning

30 min

5.2

Propositional Logic Fundamentals

35 min

5.3

Logical Equivalences and Validity

35 min

5.4

A Brief History of Logic in AI

25 min

5.5

Logic in Modern Technology

35 min

5.L

Logic Puzzles Lab

90 min

5.W

Wrap-Up and Self-Assessment

20 min

Start here with an introduction to Boolean logic — the mathematical foundation of all computing and AI reasoning.

Boolean Logic and Gates — CrashCourse Computer Science

What Is Logic?

Logic is the science of correct reasoning. In AI, it provides a formal mathematical language for representing knowledge, drawing inferences, and making decisions — all without ambiguity.

Every time you type a SQL query, every time a medical diagnostic system checks whether a patient’s symptoms satisfy a diagnostic rule, and every time a robot decides whether it can safely open a door, some form of logic is running underneath.

Logic transforms vague English statements into precise, machine-readable formulas. An AI system cannot act on "the patient might have a fever" — but it can act on Fever(patient) ∧ Temperature(patient) > 38.5.

What Is Coming

This unit builds your skills layer by layer:

  • 5.1 — Why natural language is not enough, and what formal logic gives us

  • 5.2 — Propositional logic: the five connectives, truth tables, and operator precedence

  • 5.3 — Logical equivalences, tautologies, and the concept of entailment

  • 5.4 — The 2,300-year journey from Aristotle’s syllogisms to modern AI theorem provers

  • 5.5 — First-order logic and how logic powers databases, circuits, and AI planning today

Begin Section 5.1: Why Logic? →

This work is licensed under CC BY-SA 4.0.