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図書

図書
Robert L. Causey
出版情報: Boston : Jones and Bartlett, c2001  x, 405 p. ; 24 cm
シリーズ名: Jones and Bartlett books in mathematics
所蔵情報: loading…
目次情報: 続きを見る
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:
2.

図書

図書
Robert L. Causey
出版情報: Boston : Jones and Bartlett, c1994  x, 405 p. ; 25 cm
シリーズ名: The Jones and Bartlett series in computer science
所蔵情報: loading…
目次情報: 続きを見る
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:
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