Logic, sets, and recursion

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Logic, sets, and recursion / Robert L. Causey

資料種別:: 図書
出版情報:: Boston : Jones and Bartlett, c1994
形態:: x, 405 p. ; 25 cm
シリーズ名:: The Jones and Bartlett series in computer science <BA21922108>
著者名:: Causey, Robert L.
ISBN:: 9780867204636 [086720463X]
書誌ID:: BA21922083

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Logic, sets, and recursion. Rev. ed
Robert L. Causey , Jones and Bartlett , c2001

書誌詳細

注記:

Includes bibliographical references (p. 359-364) and index

主題:

Logic, Symbolic and mathematical

言語:

英語

目次情報:

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：

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