Relational Methods for Computer Science Applications

ISBN-13: 9783662003626 / Angielski / Miękka / 2012 / 297 str.

Ewa Orlowska; Andrzej Szalas

Opis

The origins of relational theories can be found in the work of three 19th cen- tury mathematicians: Augustus de Morgan (1864, On the syllogism IV and on the logic of relations), Charles Sanders Peirce (1882, Brief description of the algebra of relatives) and Ernst Schroder (1895, Vorlesungen iiber die Al- gebra und Logik der Relative). The modern origins of the theory of relations are due to Alfred Tarski (14 January 1902, Warsaw -26 October 1983, Berke- ley). His paper' On the calculus of Relations' published in 1941 gave rise to an algebraic theory of relations which is still extensively studied. In the 1970s, the applications of relational theories to various applied sciences emerged. Nowadays relational theories are experiencing a period of extensive development, with the emergence of new theories and systems allow- ing better understanding and better use of such theories. Relational theories have been used, among others, in the following fields: * Theory of programs: program specification, program verification, mod- elling concurrency, process calculi, semantics of programming languages; * Databases: relational databases, tabular methods, dependency theory, rectangular and difunctional decomposition of databases; * Computational linguistics: relational semantics of natural languages, re- lational grammars, Lambek calculus; * Spatial reasoning: modelling of relationships between space regions; * Handling uncertainty: fuzzy relations, many-valued relations, information relations. Indeed, the concept of relation emerges again and again throughout computer science, from its theoretical foundations to very practical implementations.

Spis treści

Relations in Programming: J. Desharnais, R. Khédri, A. Mili: Interpretation of Tabular Expressions Using Arrays of Relations.- B. Dwyer: Translating Relational Programs into Prolog.- M.F. Frias, G.A. Baum, A.M. Haeberer: A Calculus for Program Contstruction Based on Fork Algebras, Design Strategies and Generic Algorithms.- M. Winter, P. Kempf: Processes as Relations. Relational Constraints: W. MacCaull: A Tableaux Procedure for the Implication Problem for Association Rules.- J. Kachniarz, A. Szalas: On a Static Verification of Integrity Constraints in Relational Databases.- Relations in Linguistics and Spatial Reasoning: I. Düntsch: Contact Relation Algebras.- J. Lambek: Relations Old and New.- M. Szczerba: Relational Models for the Nonassociative Lambek Calculus.- Relations and Uncertainty: S. Demri: Coping with Semilattices of Relations in Logics with Relative Accessibility Relations.- B. Konikowska, E. Orlowska: A Relational Formalisation of a Generic Many-Valued Modal Logic.- E. San Juan, L. Iturrioz: An Application of Standard BAO Theory to Some Abstract Information Algebras.- Theories of Relations: L. Gordeev: Proof Systems in Relation Algebra.- R. Hirsch, I. Hodkinson: Connections Between Cylindric Algebras and Relation Algebras.- Y. Kawahara: Lattices in Dedekind Categories.- Generalizations of Theories of Relations: I. Düntsch, E. Orlowska: Beyond Modalities: Sufficiency and Mixed Algebras.- A. Wolinski: Cylindric Algebras for Partial Relational Systems. Quasicylindric Algebras.

Blurb

This volume addresses all current aspects of relational methods and their applications in computer science. It presents a broad variety of fields and issues in which theories of relations provide conceptual or technical tools. The contributions address such subjects as relational methods in programming, relational constraints, relational methods in linguistics and spatial reasoning, relational modelling of uncertainty. All contributions provide the readers with new and original developments in the respective fields.
The reader thus gets an interdisciplinary spectrum of the state of the art of relational methods and implementation-oriented solutions of problems related to these areas.