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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: The present article deals with the problem whether and how the bilattice orderings of knowledge ⩽_k and truth ⩽_t might enrich the theory of rough sets. Passing to the chief idea of the paper, we develop a bilattice-theoretic generalisation of the concept of rough set to be called A-approximation. It is proved that A-approximations (induced by a topological approximation space) together with the knowledge ordering ⩽_k constitute a complete partial …order (CPO) and that the meet and join operations induced by the truth ordering ⩽_t are continuous functions with respect to ⩽_k . Crisp sets are then obtained as maximal elements of this CPO. The second part of this article deals with the categorical and algebraic properties of A-approximations induced by an Alexandroff topological space. We build a *-autonomous category of A-approximations by means of the Chu construction applied to the Heyting algebra of open sets of Alexandroff topological space. From the algebraic point of view A-approximations under ⩽_t ordering constitute a special Nelson lattice and, as a result, provide a semantics for constructive logic with strong negation. Such lattice may be obtained by means of the twist construction over a Heyting algebra which resembles very much the Chu construction. Thus A-approximations may be retrived from very elementary structures in elegant and intuitive ways. Show more
Keywords: rough set, approximation, bilattice, complete partial order, *-autonomous category, Chu construction, Nelson lattice
Citation: Fundamenta Informaticae, vol. 72, no. 1-3, pp. 421-435, 2006
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