A1 Refereed original research article in a scientific journal
Information Completeness in Nelson Algebras of Rough Sets Induced by Quasiorders
Authors: Jarvinen J, Pagliani P, Radeleczki S
Publisher: SPRINGER
Publication year: 2013
Journal: Studia Logica
Journal name in source: STUDIA LOGICA
Journal acronym: STUD LOGICA
Volume: 101
Issue: 5
First page : 1073
Last page: 1092
Number of pages: 20
ISSN: 0039-3215
DOI: https://doi.org/10.1007/s11225-012-9421-z(external)
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.
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.
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