Studia Logica 101 (5):1073-1092 (2013)
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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References found in this work BETA
An Algebraic Approach to Non-Classical Logics.Helena Rasiowa - 1974 - Warszawa, Pwn - Polish Scientific Publishers.
Some Results on Intermediate Constructive Logics.Pierangelo Miglioli, Ugo Moscato, Mario Ornaghi, Silvia Quazza & Gabriele Usberti - 1989 - Notre Dame Journal of Formal Logic 30 (4):543-562.
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