Structures with Multirelations, their Discrete Dualities and Applications

Issue title: Understanding Computers' Intelligence Celebrating the 100th Volume of Fundamenta Informaticae in Honour of Helena Rasiowa

Article type: Research Article

Authors: Düntsch., Ivo | Orłowska, Ewa | Rewitzky, Ingrid

Affiliations: Department of Computer Science, Brock University, Canada | National Institute of Telecommunications, Warsaw, Poland. E-mail: [email protected] | Department of Mathematical Sciences, University of Stellenbosch, South Africa

Abstract: In this paper we show that the problem of discrete duality can be extended beyond the clasical setting of duality between a class of algebras and a class of relational structures. Namely, for some classes of algebras, the relevant dual structures are the structures with multirelations. Several applications of multirelations will be described.

Keywords: Apartness space, dependency, discrete duality, game of choice, multirelation, nearness space, neighbourhood system, point-set relation, skill relation

DOI: 10.3233/FI-2010-264

Journal: Fundamenta Informaticae, vol. 100, no. 1-4, pp. 77-98, 2010