Information Completeness in Nelson Algebras of Rough Sets Induced by Quasiorders

: Jarvinen J, Pagliani P, Radeleczki S

Publisher: SPRINGER

: 2013

: Studia Logica

: STUDIA LOGICA

: STUD LOGICA

: 101

: 5

: 1073

: 1092

: 20

: 0039-3215

DOI: https://doi.org/10.1007/s11225-012-9421-z

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.