Studia Logica

, Volume 101, Issue 5, pp 1073–1092 | Cite as

Information Completeness in Nelson Algebras of Rough Sets Induced by Quasiorders

  • Jouni Järvinen
  • Piero Pagliani
  • Sándor Radeleczki
Article

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 E0, 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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Copyright information

© Springer Science+Business Media B.V. 2012

Authors and Affiliations

  • Jouni Järvinen
    • 1
  • Piero Pagliani
    • 2
  • Sándor Radeleczki
    • 3
  1. 1.TurkuFinland
  2. 2.Research Group on Knowledge and Communication ModelsRomaItaly
  3. 3.Institute of MathematicsUniversity of MiskolcMiskolc-EgyetemvárosHungary

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