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9780763737849

Logic, Sets And Recursion

by
  • ISBN13:

    9780763737849

  • ISBN10:

    0763737844

  • Edition: 2nd
  • Format: Hardcover
  • Copyright: 2006-01-01
  • Publisher: Jones & Bartlett

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Supplemental Materials

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Summary

This book is an introduction to mathematical logic and related topics for undergraduates. It is primarily intended for students of computer science, mathematics, and philosophy. bull; bull;Math Logic bull;Discrete Math bull;Set Theory

Table of Contents

Introduction
1(18)
The Subject Matter
1(3)
Goals and Organization
4(3)
Assumed Background Knowledge
7(8)
Sets, Numbers, and Algebra
7(3)
Functions
10(2)
Inequalities and Identity
12(3)
The Presentation
15(4)
Sentential Calculus
19(96)
Syntax of the Sentential Calculus
20(5)
Correspondence to Natural Languages
25(7)
Semantics of the Sentential Calculus
32(10)
Some Metatheoretical Concepts
42(20)
Principles for Sentential Calculus Derivations
62(16)
Adequacy and Use of Sentential Calculus Derivation Rules
78(28)
Soundness and Completeness
78(6)
Strategies for Constructing Proofs
84(8)
Sentential Calculus Derivation Examples
92(14)
Conjunctive Normal Form and Resolution Proofs
106(9)
Basic Set Theory
115(112)
Sets
115(33)
Extensionality, Predicates, and Abstraction
115(10)
Some Special Sets and Set Operations
125(23)
Relations
148(42)
General Features
148(11)
Special Kinds of Relations
159(31)
Functions
190(29)
Basic Ideas
190(7)
Compositions and Inverses
197(22)
Relational Systems
219(8)
Recursion and Mathematical Induction
227(134)
The Natural Number System
227(20)
Introduction
227(4)
Peano's Axioms and the Induction Principle
231(6)
Definition by Recursion
237(10)
Basic Arithmetic
247(25)
Some Simple Functions
247(7)
Additional Arithmetical Definitions
254(18)
Extensions of Recursive Definition and Induction
272(54)
Some Additional Applications of the Recursion Theorem
272(18)
The Well-Ordering of the Natural Numbers
290(12)
Course of Values Induction
302(6)
Two Arithmetical Algorithms
308(8)
Pitfalls of Recursion
316(10)
Nonnumerical Data
326(35)
Strings
326(7)
A Simple Treatment of Lists
333(10)
Sentential Calculus Expressions
343(2)
Stacks and Queues
345(16)
Predicate Calculus
361(98)
Syntax of the Predicate Calculus
363(13)
Semantical Aspects of the Predicate Calculus
376(24)
Interpretations and Truth
376(12)
Tautologous Sentences in Predicate Calculus
388(3)
Tautological Consequences in Predicate Calculus
391(9)
Predicate Calculus Derivations
400(31)
Derivation Rules
400(9)
Proof Strategies and Examples
409(10)
Adequacy of the Predicate Calculus Rules
419(12)
Application Example
431(8)
Identity and Function Symbols
439(12)
Extension of the Syntax
439(3)
Semantics of Predicate Calculus with Identity and Function Symbols
442(1)
Derivation Rules for Predicate Calculus with Identity and Function Symbols
443(3)
Use of Identity in Representing Information
446(5)
Formalized Theories
451(8)
Answers to Selected Exercises 459(28)
The Greek Alphabet 487(2)
Glossary of Symbols 489(6)
References 495(6)
Index 501

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