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Fork Algebras in Algebra, Logic and Computer Science

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Overview

Fork algebras are a formalism based on the relational calculus, with interesting algebraic and metalogical properties. Their representability is especially appealing in computer science, since it allows a closer relationship between their language and models. This book gives a careful account of the results and presents some applications of Fork algebras in computer science, particularly in system specification and program construction. Many applications of Fork algebras in formal methods are foreseen, and the book covers all the essentials in order to provide the reader with a better understanding.
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Product Details

  • ISBN-13: 9789810248765
  • Publisher: World Scientific Publishing Company, Incorporated
  • Publication date: 7/28/2002
  • Series: Advances in Logic Series
  • Pages: 232
  • Product dimensions: 6.30 (w) x 9.10 (h) x 0.80 (d)

Table of Contents

Preface
Ch. 1 Introduction and Motivations 1
1.1 Software Specification, Binary Relations and Fork 1
Ch. 2 Algebras of Binary Relations and Relation Algebras 5
2.1 History and Definitions 5
2.2 Arithmetical Properties 12
Ch. 3 Proper and Abstract Fork Algebras 19
3.1 On the Origin of Fork Algebras 19
3.2 Definition of the Classes 21
3.3 Arithmetical Properties 26
Ch. 4 Representability and Independence 37
4.1 Representability of Abstract Fork Algebras 38
4.2 Independence of the Axiomatization of Fork 43
Ch. 5 Interpretability of Classical First-Order Logic 49
5.1 Basic Definitions 49
5.2 Interpreting FOLE 51
Ch. 6 Algebraization of Non-Classical Logics 73
6.1 Basic Definitions and Properties 75
6.2 The Fork Logic FL 76
6.3 Modal Logics 78
6.4 Representation of Constraints in FL 80
6.5 Interpretability of Modal Logics in FL 81
6.6 A Proof Theoretical Approach 86
6.7 Interpretability of Propositional Dynamic Logic in FL 91
6.8 The Fork Logic FL' 102
6.9 A Rasiowa-Sikorski Calculus for FL' 104
6.10 A Relational Proof System for Intuitionistic Logic 115
6.11 A Relational Proof System for Minimal Intuitionistic Logic 126
6.12 Relational Reasoning in Intermediate Logics 132
Ch. 7 A Calculus for Program Construction 139
7.1 Introduction 139
7.2 Filters and Sets 141
7.3 The Relational Implication 143
7.4 Representability and Expressiveness in Program Construction 149
7.5 A Methodology for Program Construction 150
7.6 Examples 158
7.7 A D&C Algorithm for MAXSTA 192
7.8 Comparison with Previous Work 203
Bibliography 207
Index 215
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  • Anonymous

    Posted November 20, 2002

    PUEDE MEJORAR

    Errores de ortografia. Incoherencias y falta de informacion. No lo recomiendo

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