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| Preface | |
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| Introduction | |
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| The Subject Matter | |
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| Goals and Organization | |
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| Assumed Background Knowledge | |
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| The Presentation | |
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| Sentential Calculus | |
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| Syntax of the Sentential Calculus | |
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| Correspondence to Natural Languages | |
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| Semantics of the Sentential Calculus | |
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| Some Metatheoretical Concepts | |
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| Principles for Sentential Calculus Derivations | |
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| Adequacy and Use of Sentential Calculus Derivation Rules | |
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| Soundness and Completeness | |
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| Strategies for Constructing Proofs | |
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| Sentential Calculus Derivation Examples | |
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| Conjunctive Normal Form and Resolution Proofs | |
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| Basic Set Theory | |
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| Sets | |
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| Extensionality, Predicates, and Abstraction | |
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| Some Special Sets and Set Operations | |
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| Relations | |
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| General Features | |
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| Special Kinds of Relations | |
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| Functions | |
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| Basic Ideas | |
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| Compositions and Inverses | |
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| Relational Systems | |
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| Recursion and Mathematical Induction | |
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| The Natural Number System | |
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| Introduction | |
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| Peano's Axioms and the Induction Principle | |
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| Definition by Recursion | |
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| Basic Arithmetic | |
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| Some Simple Functions | |
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| Additional Arithmetical Definitions | |
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| Extensions of Recursive Definition and Induction | |
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| Some Additional Applications of the Recursion Theorem | |
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| The Well-Ordering of the Natural Numbers | |
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| Course of Values Induction | |
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| Two Arithmetical Algorithms | |
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| Pitfalls of Recursion | |
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| Non-Numerical Data | |
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| Strings | |
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| A Simple Treatment of Lists | |
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| Sentential Calculus Expressions | |
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| Stacks and Queues | |
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| Predicate Calculus | |
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| Syntax of the Predicate Calculus | |
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| Semantical Aspects of the Predicate Calculus | |
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| Interpretations and Truth | |
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| Tautologous Sentences in Predicate Calculus | |
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| Tautological Consequences in Predicate Calculus | |
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| Predicate Calculus Derivations | |
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| Derivation Rules | |
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| Proof Strategies and Examples | |
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| Adequacy of the Predicate Calculus Rules | |
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| Application Example | |
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| Identity and Function Symbols | |
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| Extension of the Syntax | |
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| Semantics of Predicate Calculus with Identity and Function Symbols | |
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| Derivation Rules for Predicate Calculus with Identity and Function Symbols | |
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| Use of Identity in Representing Information | |
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| Formalized Theories | |
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| References | |
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| Answers to Selected Exercises | |
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| The Greek Alphabet | |
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| Glossary of Symbols | |
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| Index | |