Fork Algebras in Algebra, Logic and Computer Science

Fork Algebras in Algebra, Logic and Computer Science

by Marcelo Fabian Frias
     
 

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… See more details below

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.

Product Details

ISBN-13:
9789810248765
Publisher:
World Scientific Publishing Company, Incorporated
Publication date:
07/28/2002
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. 1Introduction and Motivations1
1.1Software Specification, Binary Relations and Fork1
Ch. 2Algebras of Binary Relations and Relation Algebras5
2.1History and Definitions5
2.2Arithmetical Properties12
Ch. 3Proper and Abstract Fork Algebras19
3.1On the Origin of Fork Algebras19
3.2Definition of the Classes21
3.3Arithmetical Properties26
Ch. 4Representability and Independence37
4.1Representability of Abstract Fork Algebras38
4.2Independence of the Axiomatization of Fork43
Ch. 5Interpretability of Classical First-Order Logic49
5.1Basic Definitions49
5.2Interpreting FOLE51
Ch. 6Algebraization of Non-Classical Logics73
6.1Basic Definitions and Properties75
6.2The Fork Logic FL76
6.3Modal Logics78
6.4Representation of Constraints in FL80
6.5Interpretability of Modal Logics in FL81
6.6A Proof Theoretical Approach86
6.7Interpretability of Propositional Dynamic Logic in FL91
6.8The Fork Logic FL'102
6.9A Rasiowa-Sikorski Calculus for FL'104
6.10A Relational Proof System for Intuitionistic Logic115
6.11A Relational Proof System for Minimal Intuitionistic Logic126
6.12Relational Reasoning in Intermediate Logics132
Ch. 7A Calculus for Program Construction139
7.1Introduction139
7.2Filters and Sets141
7.3The Relational Implication143
7.4Representability and Expressiveness in Program Construction149
7.5A Methodology for Program Construction150
7.6Examples158
7.7A D&C Algorithm for MAXSTA192
7.8Comparison with Previous Work203
Bibliography207
Index215

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