Fork Algebras in Algebra, Logic and Computer Science.
Title:
Fork Algebras in Algebra, Logic and Computer Science.
Author:
Frias, Marcelo Fabián.
ISBN:
9789812777928
Personal Author:
Physical Description:
1 online resource (230 pages)
Series:
Advances in Logic ; v.2
Advances in Logic
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 -- 6.10.3.1 Example -- 6.11 A Relational Proof System for Minimal Intuitionistic Logic -- 6.12 Relational Reasoning in Intermediate Logics -- 6.12.1 Method 1 -- 6.12.2 Method 2 -- 6.12.3 Method 3 -- Chapter 7 A Calculus for Program Construction -- 7.1 Introduction -- 7.2 Filters and Sets -- 7.3 The Relational Implication.
7.4 Representability and Expressiveness in Program Construction -- 7.5 A Methodology for Program Construction -- 7.6 Examples -- 7.6.1 First Example -- 7.6.1.1 Finding the Minimum Element in a List -- 7.6.1.2 Finding the Minimum Common Ancestor -- 7.6.2 Second Example -- 7.6.2.1 Finding the Contiguous Sublists of Maximum Sum -- 7.6.2.2 Finding the Longest Plateau -- 7.7 A D&C Algorithm for MAXSTA -- 7.8 Comparison with Previous Work -- Bibliography -- Index.
Abstract:
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 better understanding. Sample Chapter(s). Chapter 1: Introduction and Motivations (110 KB). Contents: Introduction and Motivations; Algebras of Binary Relations and Relation Algebras; Proper and Abstract Fork Algebras; Representability and Independence; Interpretability of Classical First-Order Logic; Algebraization of Non-Classical Logics; A Calculus for Program Construction. Readership: Graduate students and researchers using relational methods in computer science.
Local Note:
Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2017. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.
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Electronic Access:
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