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Fundamenta Informaticae is an international journal publishing original research results in all areas of theoretical computer science. Papers are encouraged contributing:
- solutions by mathematical methods of problems emerging in computer science
- solutions of mathematical problems inspired by computer science.
Topics of interest include (but are not restricted to): theory of computing, complexity theory, algorithms and data structures, computational aspects of combinatorics and graph theory, programming language theory, theoretical aspects of programming languages, computer-aided verification, computer science logic, database theory, logic programming, automated deduction, formal languages and automata theory, concurrency and distributed computing, cryptography and security, theoretical issues in artificial intelligence, machine learning, pattern recognition, algorithmic game theory, bioinformatics and computational biology, quantum computing, probabilistic methods, & algebraic and categorical methods.
Authors: Wolski, Marcin
Article Type: Research Article
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. Show more
Citation: Fundamenta Informaticae, vol. 109, no. 3, pp. 355-368, 2011
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