Lattice-Based Paraconsistent Logic

  • Wendy MacCaull
  • Dimiter Vakarelov
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3929)


In this paper we describe a procedure for developing models and associated proof systems for two styles of paraconsistent logic. We first give an Urquhart-style representation of bounded not necessarily discrete lattices using (grill, cogrill) pairs. From this we develop Kripke semantics for a logic permitting 3 truth values: true, false and both true and false. We then enrich the lattice by adding a unary operation of negation that is involutive and antimonotone and show that the representation may be extended to these lattices. This yields Kripke semantics for a nonexplosive 3-valued logic with negation.


paraconsistent logic lattice representation Kripke semantics negation graded information multi-valued logic 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Wendy MacCaull
    • 1
  • Dimiter Vakarelov
    • 2
  1. 1.Department of Mathematics, Statistics and Computer ScienceSt.Francis Xavier UniversityAntigonishCanada
  2. 2.Department of Mathematical LogicSofia UniversitySofiaBulgaria

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