Introduction to Logic Tools for Thought   Help Lessons Chapters Dictionary Tools Preface Preview Sets, Functions, Relations Algebra - Khan Academy Acknowledgements   Lesson 1 - Introduction Section 1.1 - Video 1.1 - Introduction Section 1.2 - Video 1.2 - Logical Sentences Section 1.3 - Video 1.3 - Logical Entailment Section 1.4 - Video 1.4 - Logical Proofs Section 1.5 - Video 1.5 - Symbolic Logic Section 1.6 - Video 1.6 - Automation Section 1.7 - Video 1.7 - Conclusion Exercise 1.1 Exercise 1.2 Exercise 1.3 Exercise 1.4 Exercise 1.5 Exercise 1.6 Exercise 1.7 Extra - Alice Extra - Formal Logic Puzzle - Locks (very easy)   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 Extra - The Big Game Extra - Labyrinth Puzzle Puzzle - Coins   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 Section 3.7 - Equivalence Rewritings Exercise 3.1 Exercise 3.2 Exercise 3.3 Exercise 3.4 Exercise 3.5 Exercise 3.6 Extra - Satisfiability Extra - Whodunnit Extra - Digital Circuits Tool - Digital Circuit Builder Tool - Babbage Tool - Boole Tool - Quine Puzzle - Rotors   Lesson 4 - Direct Proofs Section 4.1 - Introduction Section 4.2 - Axiom Schemas Section 4.3 - Rules of Inference Section 4.4 - Direct Proofs Section 4.5 - Proof Systems Section 4.6 - Soundness and Completeness Exercise 4.1 Exercise 4.2 Exercise 4.3 Exercise 4.4 Exercise 4.5 Tool - Hilbert Propositional Hilbert Proofs Puzzle - Wine   Lesson 5 - Natural Deduction Section 5.1 - Introduction Section 5.2 - Conditional Proofs Section 5.3 - Fitch Section 5.4 - Soundness and Completeness Section 5.5 - Reasoning Tips Exercise 5.1 Exercise 5.2 Exercise 5.3 Exercise 5.4 Exercise 5.5 Exercise 5.6 Exercise 5.7 Exercise 5.8 Exercise 5.9 Exercise 5.10 Exercise 5.11 Exercise 5.12 Exercise 5.13 Exercise 5.14 Tool - Fitch Propositional Fitch Proofs Puzzle - Counterfeit (easy)   Lesson 6 - Resolution Proofs Section 6.1 - Introduction Section 6.2 - Clausal Form Section 6.3 - Resolution Principle Section 6.4 - Resolution Reasoning Exercise 6.1 Exercise 6.2 Exercise 6.3 Exercise 6.4 Extra - Box Logic Tool - Stickel Tool - Robinson Puzzle - Pills   Lesson 7 - Relational Logic Section 7.1 - Introduction Section 7.2 - Syntax Section 7.3 - Semantics Section 7.4 - Evaluation Section 7.5 - Satisfaction Section 7.6 - Sorority World Section 7.7 - Blocks World Section 7.8 - Modular Arithmetic Exercise 7.1 Exercise 7.2 Exercise 7.3 Exercise 7.4 Extra - Sorority Life Extra - Minefinder Extra - Minefield Extra - Logicians Puzzle - Cards   Lesson 8 - Relational Analysis Section 8.1 - Introduction Section 8.2 - Logical Properties Section 8.3 - Logical Relationships Section 8.4 - Relational Logic and Propositional Logic Exercise 8.1 Exercise 8.2 Exercise 8.3 Extra - Relational Satisfiability Tool - Quine Puzzle - Safecracking   Lesson 9 - Model Checking Section 9.1 - Introduction Section 9.2 - Truth Tables Section 9.3 - Boolean Models Section 9.4 - Non-Boolean Models Exercise 9.1 Exercise 9.2 Exercise 9.3 Extra - Train Tracks Extra - Mineplanner Extra - Neighborhood Tool - Clarke Puzzle - Prisoners   Lesson 10 - Fitch Proofs Section 10.1 - Introduction Section 10.2 - Rules for Quantifiers Section 10.3 - Examples Section 10.4 - Examples Exercise 10.1 Exercise 10.2 Exercise 10.3 Exercise 10.4 Exercise 10.5 Exercise 10.6 Exercise 10.7 Exercise 10.8 Exercise 10.9 Exercise 10.10 Extra - Jeopardy Tool - Fitch Relational Fitch Proofs Puzzle - Chessboard (difficult)   Lesson 11 - Functional Logic Section 11.1 - Introduction Section 11.2 - Syntax and Semantics Section 11.3 - Evaluation and Satisfaction Section 11.4 - Peano Arithmetic Section 11.5 - Linked Lists Section 11.6 - Pseudo English Section 11.7 - Metalevel Logic Exercise 11.1 Exercise 11.2 Exercise 11.3 Exercise 11.4 Exercise 11.5 Puzzle - Logicians   Lesson 12 - Fitch Proofs Section 12.1 - Introduction Section 12.2 - Example - Interactive Logic Grids Section 12.3 - Non-Compactness and Incompleteness Section 12.4 - Undecidability Exercise 12.1 Exercise 12.2 Extra - Blocks World Dynamics Tool - Fitch Puzzle - Nim   Lesson 13 - Induction Section 13.1 - Introduction Section 13.2 - Domain Closure Section 13.3 - Linear Induction Section 13.4 - Tree Induction Section 13.5 - Structural Induction Section 13.6 - Multidimensional Induction Section 13.7 - Embedded Induction Exercise 13.1 Exercise 13.2 Exercise 13.3 Exercise 13.4 Exercise 13.5 Exercise 13.6 Tool - Fitch Functional Fitch Proofs Puzzle - Zoom   Lesson 14 - Resolution Section 14.1 - Introduction Section 14.2 - Clausal Form Section 14.3 - Unification Section 14.4 - Resolution Principle Section 14.5 - Resolution Reasoning Section 14.6 - Unsatisfiability Section 14.7 - Logical Entailment Section 14.8 - Answer Extraction Section 14.9 - Strategies Exercise 14.1 Exercise 14.2 Exercise 14.3 Exercise 14.4 Exercise 14.5 Exercise 14.6 Exercise 14.7 Exercise 14.8 Exercise 14.9 Exercise 14.10 Puzzle - Nations   Lesson 15 - Equality Section 15.1 - Introduction Section 15.2 - Properties of Equality Section 15.3 - Substitution Section 15.4 - Fitch With Equality Section 15.5 - Example - Group Theory Exercise 15.1 Exercise 15.2 Exercise 15.3 Exercise 15.4 Exercise 15.5 Tool - Fitch Fitch Equality Proofs Puzzle - Suarez   Lesson 16 - First-Order Logic Section 16.1 - Introduction Section 16.2 - Conceptualization Section 16.3 - Semantics Section 16.4 - Blocks World Section 16.5 - Arithmetic Section 16.6 - Properties Section 16.7 - Logical Entailment Puzzle - Quiz   Lesson 17 - Conclusion Section 17.1 - Introduction Section 17.2 - Review Section 17.3 - Extensions Puzzle - Enlightenment   Supplementary Material Resolution Herbrand Manifesto   Use the arrow keys to navigate. 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