A1 Vertaisarvioitu alkuperäisartikkeli tieteellisessä lehdessä
Information Completeness in Nelson Algebras of Rough Sets Induced by Quasiorders
Tekijät: Jarvinen J, Pagliani P, Radeleczki S
Kustantaja: SPRINGER
Julkaisuvuosi: 2013
Journal: Studia Logica
Tietokannassa oleva lehden nimi: STUDIA LOGICA
Lehden akronyymi: STUD LOGICA
Vuosikerta: 101
Numero: 5
Aloitussivu: 1073
Lopetussivu: 1092
Sivujen määrä: 20
ISSN: 0039-3215
DOI: https://doi.org/10.1007/s11225-012-9421-z
Tiivistelmä
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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