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Information Completeness in Nelson Algebras of Rough Sets Induced by Quasiorders

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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.

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Authors and Affiliations

  1. Sirkkalankatu 6, 20520, Turku, Finland

    Jouni Järvinen

  2. Research Group on Knowledge and Communication Models, Via imperia 6, 00161, Roma, Italy

    Piero Pagliani

  3. Institute of Mathematics, University of Miskolc, 3515, Miskolc-Egyetemváros, Hungary

    Sándor Radeleczki

Authors
  1. Jouni Järvinen
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  2. Piero Pagliani
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  3. Sándor Radeleczki
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Correspondence to Jouni Järvinen.

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Presented by Andrzej Indrzejczak

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Järvinen, J., Pagliani, P. & Radeleczki, S. Information Completeness in Nelson Algebras of Rough Sets Induced by Quasiorders. Stud Logica 101, 1073–1092 (2013). https://doi.org/10.1007/s11225-012-9421-z

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