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Introduction

• 90 = 100: A Proof
• the need for proofs
• defining a proof

Propositional Logic

A formal vocabulary

• propositions
• formulas

Reasoning with truth tables

• using truth tables
• the limitations of truth tables

Reasoning with equivalences

• propositional equivalences
• normal forms
• soundness and completeness

Reasoning with inference rules

• propositional inference rules
• using subproofs
• the soundness and completeness of inference rules
• proofs and programming
• conclusions
• Exercises for Propositional Logic I
• Exercises for Propositional Logic II

Relations and Models

• relations
• properties of relations
• interpretations
• Nonstandard Interpretations (optional)
• modeling with relations

First-Order Logic

A formal vocabulary

• syntax and semantics of quantifiers
• bound variables, free variables
• normal forms revisited

Reasoning with equivalences

• first-order equivalences

Reasoning with inference rules

• first-order inference rules
• Exercises for First-Order Logic

Conclusion, Acknowledgements

• Logic: Looking Back
• Acknowledgements

Appendices and Reference Sheets

• propositional equivalences
• propositional inference rules
• first-order equivalences
• first-order inference rules
• propositional axioms for WaterWorld
• first-order axioms for WaterWorld
• browser support