Introduction to Logic Tools
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Preface
Preview
Sets, Functions, Relations
Algebra - Khan Academy
 
Lesson 1 - Introduction
Lesson 1.1 - Introduction
Lesson 1.2 - Sorority World
Lesson 1.3 - Logical Sentences
Lesson 1.4 - Logical Entailment
Lesson 1.5 - Logical Proofs
Lesson 1.6 - Formalization
Lesson 1.7 - Automation
Lesson 1.8 - Reading Guide
Exercise 1.1
Exercise 1.2
Exercise 1.3
Exercise 1.4
Extra - Alice in Wonderland
Extra - Penguins
 
Lesson 2 - Propositional Logic
Lesson 2.1 - Introduction
Lesson 2.2 - Syntax
Lesson 2.3 - Semantics
Lesson 2.4 - Evaluation
Lesson 2.5 - Satisfaction
Lesson 2.6 - Example - Natural Language
Lesson 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
Extra - The Big Game
Extra - Labyrinth Puzzle
 
Lesson 3 - Propositional Analysis
Lesson 3.1 - Introduction
Lesson 3.2 - Logical Properties
Lesson 3.3 - Logical Equivalence
Lesson 3.4 - Logical Entailment
Lesson 3.5 - Logical Consistency
Lesson 3.6 - Properties and Relationships
Lesson 3.7 - Equivalence Rewritings
Exercise 3.1
Exercise 3.2
Exercise 3.3
Exercise 3.4
Exercise 3.5
Exercise 3.6
Extra - Whodunnit
Extra - Digital Circuits
 
Lesson 4 - Propositional Proofs
Lesson 4.1 - Introduction
Lesson 4.2 - Linear Reasoning
Lesson 4.3 - Hypothetical Reasoning
Lesson 4.4 - Fitch
Lesson 4.5 - Reasoning Tips
Lesson 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
Lesson 5.1 - Introduction
Lesson 5.2 - Clausal Form
Lesson 5.3 - Resolution Principle
Lesson 5.4 - Resolution Reasoning
Exercise 5.1
Exercise 5.2
Exercise 5.3
Exercise 5.4
Extra - Box Logic
 
Lesson 6 - Relational Logic
Lesson 6.1 - Introduction
Lesson 6.2 - Syntax
Lesson 6.3 - Semantics
Lesson 6.4 - Evaluation
Lesson 6.5 - Satisfaction
Lesson 6.6 - Sorority World
Lesson 6.7 - Blocks World
Lesson 6.8 - Modular Arithmetic
Lesson 6.9 - Logical Properties
Lesson 6.10 - Logical Entailment
Lesson 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
Extra - Sorority Life
Extra - Relational Satisfiability
Extra - Train Tracks
Extra - Minefinder
Extra - Minefield
Extra - Mineplanner
Extra - Pelican Hunters
Extra - Logicians
 
Lesson 7 - Relational Analysis
Lesson 7.1 - Introduction
Lesson 7.2 - Truth Tables
Lesson 7.3 - Semantic Trees
Lesson 7.4 - Boolean Models
Lesson 7.5 - Non-Boolean Models
Exercise 7.1
Exercise 7.2
Exercise 7.3
 
Lesson 8 - Relational Proofs
Lesson 8.1 - Introduction
Lesson 8.2 - Rules for Universal Quantifiers
Lesson 8.3 - Rules for Existential Quantifiers
Lesson 8.4 - Domain Closure
Lesson 8.5 - Example
Lesson 8.6 - Example
Lesson 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 - Relational Resolution
Lesson 9.1 - Introduction
Lesson 9.2 - Clausal Form
Lesson 9.3 - Unification
Lesson 9.4 - Resolution Principle
Lesson 9.5 - Resolution Reasoning
Lesson 9.6 - Unsatisfiability
Lesson 9.7 - Logical Entailment
Lesson 9.8 - Answer Extraction
Lesson 9.9 - Strategies
Exercise 9.1
Exercise 9.2
Exercise 9.3
Exercise 9.4
Exercise 9.5
Exercise 9.6
Exercise 9.7
Exercise 9.8
Exercise 9.9
Exercise 9.10
 
Lesson 10 - Herbrand Logic
Lesson 10.1 - Introduction
Lesson 10.2 - Syntax and Semantics
Lesson 10.3 - Evaluation and Satisfaction
Lesson 10.4 - Peano Arithmetic
Lesson 10.5 - Linked Lists
Lesson 10.6 - Pseudo English
Lesson 10.7 - Metalevel Logic
Exercise 10.1
Exercise 10.2
Exercise 10.3
Exercise 10.4
Exercise 10.5
 
Lesson 11 - Herbrand Proofs
Lesson 11.1 - Introduction
Lesson 11.2 - Non-Compactness and Incompleteness
Lesson 11.3 - Undecidability
Extra - Blocks World Programs
 
Lesson 12 - Induction
Lesson 12.1 - Introduction
Lesson 12.2 - Domain Closure
Lesson 12.3 - Linear Induction
Lesson 12.4 - Tree Induction
Lesson 12.5 - Structural Induction
Lesson 12.6 - Multidimensional Induction
Lesson 12.7 - Embedded Induction
Exercise 12.1
Exercise 12.2
Exercise 12.3
Exercise 12.4
Exercise 12.5
Exercise 12.6
 
Supplementary Material
Satisfiability
Equality
First-Order Logic
Herbrand Manifesto