Studia Logica

, Volume 101, Issue 5, pp 1073-1092

First online:

Information Completeness in Nelson Algebras of Rough Sets Induced by Quasiorders

  • Jouni JärvinenAffiliated with Email author 
  • , Piero PaglianiAffiliated withResearch Group on Knowledge and Communication Models
  • , Sándor RadeleczkiAffiliated withInstitute of Mathematics, University of Miskolc

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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.


Rough sets Nelson algebras Quasiorders (preorders) Knowledge representation Boolean congruence Glivenko congruence Logics with strong negation