Preface |
Introduction |
The Subject Matter / 1: |
Goals and Organization / 2: |
Assumed Background Knowledge / 3: |
The Presentation / 4: |
Sentential Calculus / Chapter 1.: |
Syntax of the Sentential Calculus / 1.1: |
Correspondence to Natural Languages / 1.2: |
Semantics of the Sentential Calculus / 1.3: |
Some Metatheoretical Concepts / 1.4: |
Principles for Sentential Calculus Derivations / 1.5: |
Adequacy and Use of Sentential Calculus Derivation Rules / 1.6: |
Soundness and Completeness / 1.6.1: |
Strategies for Constructing Proofs / 1.6.2: |
Sentential Calculus Derivation Examples / 1.6.3: |
Conjunctive Normal Form and Resolution Proofs / 1.7: |
Basic Set Theory / Chapter 2.: |
Sets / 2.1: |
Extensionality, Predicates, and Abstraction / 2.1.1: |
Some Special Sets and Set Operations / 2.1.2: |
Relations / 2.2: |
General Features / 2.2.1: |
Special Kinds of Relations / 2.2.2: |
Functions / 2.3: |
Basic Ideas / 2.3.1: |
Compositions and Inverses / 2.3.2: |
Relational Systems / 2.4: |
Recursion and Mathematical Induction / Chapter 3.: |
The Natural Number System / 3.1: |
Peano's Axioms and the Induction Principle / 3.1.1: |
Definition by Recursion / 3.1.3: |
Basic Arithmetic / 3.2: |
Some Simple Functions / 3.2.1: |
Additional Arithmetical Definitions / 3.2.2: |
Extensions of Recursive Definition and Induction / 3.3: |
Some Additional Applications of the Recursion Theorem / 3.3.1: |
The Well-Ordering of the Natural Numbers / 3.3.2: |
Course of Values Induction / 3.3.3: |
Two Arithmetical Algorithms / 3.3.4: |
Pitfalls of Recursion / 3.3.5: |
Non-Numerical Data / 3.4: |
Strings / 3.4.1: |
A Simple Treatment of Lists / 3.4.2: |
Sentential Calculus Expressions / 3.4.3: |
Stacks and Queues / 3.4.4: |
Predicate Calculus / Chapter 4.: |
Syntax of the Predicate Calculus / 4.1: |
Semantical Aspects of the Predicate Calculus / 4.2: |
Interpretations and Truth / 4.2.1: |
Tautologous Sentences in Predicate Calculus / 4.2.2: |
Tautological Consequences in Predicate Calculus / 4.2.3: |
Predicate Calculus Derivations / 4.3: |
Derivation Rules / 4.3.1: |
Proof Strategies and Examples / 4.3.2: |
Adequacy of the Predicate Calculus Rules / 4.3.3: |
Application Example / 4.4: |
Identity and Function Symbols / 4.5: |
Extension of the Syntax / 4.5.1: |
Semantics of Predicate Calculus with Identity and Function Symbols / 4.5.2: |
Derivation Rules for Predicate Calculus with Identity and Function Symbols / 4.5.3: |
Use of Identity in Representing Information / 4.5.4: |
Formalized Theories / 4.6: |
References |
Answers to Selected Exercises |
The Greek Alphabet / Chapter 1: |
Glossary of Symbols |
Index |
Preface |
Introduction |
The Subject Matter / 1: |
Goals and Organization / 2: |
Assumed Background Knowledge / 3: |
The Presentation / 4: |