Foundations of Computing: System Development with Set Theory and Logic / Edition 1

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Overview

Set theory and logic are the twin pillars of computing science. Their mastery is an essential part of the software engineer's education. This book provides a clear introduction to the key ideas of these two subjects and shows how they can be applied successfully in formal system development.

Highlights of the book include:

  • A presentation of set theory as a modelling language of universal applicability
  • A wealth of practical examples demonstrating the remarkable simplicity and naturalness of set theory as a description tool
  • A description of logic as a formal language, and as a simple way of introducing the key concepts of formal syntax, semantics and deduction calculus
  • A practical methodology of system development based on set theory and illustrated by several substantial case studies

The book starts from first principles and requires no prior knowledge of mathematics. It will be equally valuable for students of computing science and software engineers wishing to develop the skills required to apply formal methods successfully.

Written for professionals learning the field of discrete mathematics, this book provides the necessary foundations of computer science without requiring excessive mathematical prerequisites. Using a balanced approach of theory and examples, software engineers will find it a refreshing treatment of applications in programming.

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Editorial Reviews

Booknews
An introduction to set theory and logic and their applications in formal system development, emphasizing set theory as a modeling language of universal applicability. Analyzes logic as a formal language, and covers key concepts of formal syntax, semantics, and deduction calculus. Includes examples and case studies. Annotation c. Book News, Inc., Portland, OR (booknews.com)
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Product Details

  • ISBN-13: 9780201544299
  • Publisher: Addison-Wesley
  • Publication date: 1/28/1994
  • Series: International Computer Science Ser.
  • Edition number: 1
  • Pages: 704
  • Product dimensions: 6.77 (w) x 9.26 (h) x 1.44 (d)

Table of Contents

Preface
List of Symbols
Pt. 1 Overview 1
1 A View of System Development 7
Pt. 2 Set Theory and Induction 33
2 Sets and Basic Set Operations 35
3 Relations and Functions 89
4 Induction and Recursion 179
Pt. 3 Symbolic Logic 239
5 Introduction to Symbolic Logic 241
6 Propositional Logic 249
7 First-order Predicate Logic 281
8 Formal Deduction in First-order Logic 321
9 Formal Proofs in Set Theory 369
Pt. 4 Feature Notation, Lists and Trees 393
10 Complex Models and Feature Notation 395
11 Families and Lists 433
12 Forests and Trees 479
Pt. 5 Application Case Studies 527
13 Introduction to Application Case Studies 529
14 An Evolving Set Model 539
15 An Evolving Dictionary Model 549
16 A Tree Editor (TEd) 565
17 A General Resource Allocation Model (ResAll) 599
References 647
Index 649
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