Folk algebras in algebra : logic and computer science / Marcelo Fabian Frias.

Format:

Book

Author/Creator:

Frias, Marcelo Fabián, 1968-

Series:

Advances in logic ; v. 2.

Advances in logic ; v. 2

Language:

English

Subjects (All):

Computer science--Mathematics.

Computer science.

Logic, Symbolic and mathematical.

Physical Description:

1 online resource (230 p.)

Edition:

1st ed.

Place of Publication:

River Edge, NJ : World Scientific, 2002.

Language Note:

English

Summary:

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 can be applied in many ways, and the book covers all the essentials in order to provide the reader with a

Contents:

Contents ; Preface ; Chapter 1 Introduction and Motivations ; 1.1 Software Specification Binary Relations and Fork ; Chapter 2 Algebras of Binary Relations and Relation Algebras ; 2.1 History and Definitions ; 2.2 Arithmetical Properties ; Chapter 3 Proper and Abstract Fork Algebras

3.1 On the Origin of Fork Algebras 3.2 Definition of the Classes ; 3.3 Arithmetical Properties ; Chapter 4 Representability and Independence ; 4.1 Representability of Abstract Fork Algebras ; 4.2 Independence of the Axiomatization of Fork

Chapter 5 Interpretability of Classical First-Order Logic 5.1 Basic Definitions ; 5.2 Interpreting FOLE ; Chapter 6 Algebraization of Non-Classical Logics ; 6.1 Basic Definitions and Properties ; 6.2 The Fork Logic FL ; 6.3 Modal Logics ; 6.4 Representation of Constraints in FL

6.5 Interpretability of Modal Logics in FL 6.6 A Proof Theoretical Approach ; 6.7 Interpretability of Propositional Dynamic Logic in FL ; 6.8 The Fork Logic FL' ; 6.8.1 Syntax of FL' ; 6.8.2 Semantics of FL' ; 6.9 A Rasiowa-Sikorski Calculus for FL'

6.9.1 The Deduction System for FL' 6.9.2 Soundness and Completeness of the Calculus FLC ; 6.9.3 Examples of Proofs in the Calculus FLC ; 6.10 A Relational Proof System for Intuitionistic Logic ; 6.10.1 Intuitionistic Logic ; 6.10.2 Interpretability of Intuitionistic Logic in FL'

6.10.3 A Fork Logic Calculus for Intuitionistic Logic

Notes:

Description based upon print version of record.

Includes bibliographical references (p. 207-213) and index.

ISBN:

9789812777928

981277792X

OCLC:

881611050