Information Completeness in Nelson Algebras of Rough Sets Induced by Quasiorders

Studia Logica 101 (5):1073-1092 (2013)
Abstract
In this paper, we give an algebraic completeness theorem for constructive logic with strong negation in terms of finite rough set-based Nelson algebras determined by quasiorders. We show how for a quasiorder R, its rough set-based Nelson algebra can be obtained by applying Sendlewski’s well-known construction. We prove that if the set of all R-closed elements, which may be viewed as the set of completely defined objects, is cofinal, then the rough set-based Nelson algebra determined by the quasiorder R forms an effective lattice, that is, an algebraic model of the logic E 0, which is characterised by a modal operator grasping the notion of “to be classically valid”. We present a necessary and sufficient condition under which a Nelson algebra is isomorphic to a rough set-based effective lattice determined by a quasiorder
Keywords Rough sets  Nelson algebras  Quasiorders (preorders)  Knowledge representation  Boolean congruence  Glivenko congruence  Logics with strong negation
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DOI 10.1007/s11225-012-9421-z
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References found in this work BETA
Situations and Attitudes.Jon Barwise & John Perry - 1981 - Journal of Philosophy 78 (11):668-691.
An Algebraic Approach to Non-Classical Logics.Helena Rasiowa - 1974 - Warszawa, Pwn - Polish Scientific Publishers.
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Nelson Algebras Through Heyting Ones: I.Andrzej Sendlewski - 1990 - Studia Logica 49 (1):105-126.

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