Incomplete and Nondeterministic Information Systems: Object-Directed Semantics for Descriptor Languages

Issue title: Concurrency Specification and Programming (CS&P)

Article type: Research Article

Authors: Wolski, Marcin

Affiliations: Department of Logic and Philosophy of Science, Maria Curie-Skłodowska University, Poland. [email protected]

Note: [] Address for correspondence: Department of Logic and Philosophy of Science, Maria Curie-Skłodowska University, Poland

Abstract: In the paper we discuss logical approaches to incomplete and/or nondeterministic data. As is well-known, complete and deterministic information systems induce indiscernibility relations and the lower and upper approximations regarded as operators obey the laws of S5 modal system. In the case of incomplete and/or nondeterministic systems, this modal approach yields a few more binary relations on the set of objects (e.g. NIL-structures and NIL-logics). Anyway, in both cases, there are relations which play a dominant role. The main idea of this study is to shift the focus from relations to objects – that is why we use the term object-directed. Following well-established traditions from modal logics, we would like to consider objects with empty or non-single attribute values as a special kind of worlds. In consequence, in the object-directed approach there would be two sorts of objects and (usually) one relation in contrast to the relation-directed approach where we have one sort of objects and a number of relations. In the first part of our paper we shall discuss a global kind of non-normality and show how rough approximations can be linked to weak modal systems. In the second part we shall consider a local kind of non-normality; this time we use a multi-valued modal system Q introduced by A. N. Prior. The key idea offered by the paper is to regard incomplete and/or nondeterministic information systems as a source of non-normal models for (modal) descriptor languages.

DOI: 10.3233/FI-2011-516

Journal: Fundamenta Informaticae, vol. 109, no. 3, pp. 355-368, 2011