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図書
図書
1. Logic, sets, and recursion
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：
2.

図書
図書
2. Logic, sets, and recursion. Rev. ed
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：
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