Introduction to Logic Tools
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Preface
Preview
Sets, Functions, Relations
Algebra - Khan Academy
 
Lesson 1 - Introduction
Section 1.1 - Introduction
Section 1.2 - Sorority World
Section 1.3 - Logical Sentences
Section 1.4 - Logical Entailment
Section 1.5 - Logical Proofs
Section 1.6 - Formalization
Section 1.7 - Automation
Section 1.8 - Reading Guide
Exercise 1.1
Exercise 1.2
Exercise 1.3
Exercise 1.4
Alice in Wonderland
Cartoon - Penguins
 
Lesson 2 - Propositional Logic
Section 2.1 - Introduction
Section 2.2 - Syntax
Section 2.3 - Semantics
Section 2.4 - Evaluation
Section 2.5 - Satisfaction
Section 2.6 - Example - Natural Language
Section 2.7 - Example - Digital Circuits
Exercise 2.1
Exercise 2.2
Exercise 2.3
Exercise 2.4
Exercise 2.5
Exercise 2.6
Exercise 2.7
The Big Game
Cartoon - Labyrinth Puzzle
 
Lesson 3 - Propositional Analysis
Section 3.1 - Introduction
Section 3.2 - Logical Properties
Section 3.3 - Logical Equivalence
Section 3.4 - Logical Entailment
Section 3.5 - Logical Consistency
Section 3.6 - Properties and Relationships
Exercise 3.1
Exercise 3.2
Exercise 3.3
Exercise 3.4
Exercise 3.5
Exercise 3.6
Whodunnit
Digital Circuits
 
Lesson 4 - Propositional Proofs
Section 4.1 - Introduction
Section 4.2 - Linear Reasoning
Section 4.3 - Hypothetical Reasoning
Section 4.4 - Fitch
Section 4.5 - Reasoning Tips
Section 4.6 - Soundness and Completeness
Exercise 4.1
Exercise 4.2
Exercise 4.3
Exercise 4.4
Exercise 4.5
Exercise 4.6
Exercise 4.7
Exercise 4.8
Exercise 4.9
Exercise 4.10
Exercise 4.11
Exercise 4.12
Exercise 4.13
Exercise 4.14
 
Lesson 5 - Propositional Resolution
Section 5.1 - Introduction
Section 5.2 - Clausal Form
Section 5.3 - Resolution Principle
Section 5.4 - Resolution Reasoning
Exercise 5.1
Exercise 5.2
Exercise 5.3
Exercise 5.4
Box Logic
 
Lesson 6 - Relational Logic
Section 6.1 - Introduction
Section 6.2 - Syntax
Section 6.3 - Semantics
Section 6.4 - Evaluation
Section 6.5 - Satisfaction
Section 6.6 - Sorority World
Section 6.7 - Blocks World
Section 6.8 - Modular Arithmetic
Section 6.9 - Logical Properties
Section 6.10 - Logical Entailment
Section 6.11 - Relational Logic and Propositional Logic
Exercise 6.1
Exercise 6.2
Exercise 6.3
Exercise 6.4
Exercise 6.5
Exercise 6.6
Exercise 6.7
Game - Sorority Life
Game - Train Tracks
Game - Minefinder
Game - Minefield
Game - Mineplanner
Game - Pelican Hunters
Cartoon - Logicians
 
Lesson 7 - Relational Analysis
Section 7.1 - Introduction
Section 7.2 - Truth Tables
Section 7.3 - Semantic Trees
Section 7.4 - Boolean Models
Section 7.5 - Non-Boolean Models
Exercise 7.1
Exercise 7.2
Exercise 7.3
 
Lesson 8 - Relational Proofs
Section 8.1 - Introduction
Section 8.2 - Rules for Universal Quantifiers
Section 8.3 - Rules for Existential Quantifiers
Section 8.4 - Domain Closure
Section 8.5 - Example
Section 8.6 - Example
Section 8.7 - Example
Exercise 8.1
Exercise 8.2
Exercise 8.3
Exercise 8.4
Exercise 8.5
Exercise 8.6
Exercise 8.7
Exercise 8.8
 
Lesson 9 - Herbrand Logic
Section 9.1 - Introduction
Section 9.2 - Syntax and Semantics
Section 9.3 - Evaluation and Satisfaction
Section 9.4 - Peano Arithmetic
Section 9.5 - Linked Lists
Section 9.6 - Pseudo English
Section 9.7 - Metalevel Logic
Section 9.8 - Undecidability
Exercise 9.1
Exercise 9.2
Exercise 9.3
Exercise 9.4
Exercise 9.5
 
Lesson 10 - Herbrand Proofs
Section 10.1 - Introduction
Section 10.2 - Non-Compactness and Incompleteness
Blocks World Programs
 
Lesson 11 - Induction
Section 11.1 - Introduction
Section 11.2 - Domain Closure
Section 11.3 - Linear Induction
Section 11.4 - Tree Induction
Section 11.5 - Structural Induction
Section 11.6 - Multidimensional Induction
Section 11.7 - Embedded Induction
Exercise 11.1
Exercise 11.2
Exercise 11.3
Exercise 11.4
Exercise 11.5
Exercise 11.6
 
Lesson 12 - Resolution
Section 12.1 - Introduction
Section 12.2 - Clausal Form
Section 12.3 - Unification
Section 12.4 - Resolution Principle
Section 12.5 - Resolution Reasoning
Section 12.6 - Unsatisfiability
Section 12.7 - Logical Entailment
Section 12.8 - Answer Extraction
Section 12.9 - Strategies
Exercise 12.1
Exercise 12.2
Exercise 12.3
Exercise 12.4
Exercise 12.5
Exercise 12.6
Exercise 12.7
Exercise 12.8
Exercise 12.9
Exercise 12.10
 
Supplementary Material
Satisfiability
Equality
First-Order Logic
Herbrand Manifesto