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Lattice-Based Paraconsistent Logic

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Relational Methods in Computer Science (RelMiCS 2005)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 3929))

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Abstract

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.

This work was performed within the framework of the COST Action 274, entitled: ”Theory and Applications of Relational Structures as Knowledge Instruments” (www.tarski.org). Both authors were supported by a NATO Science and Technology Collaborative Linkages Grant.

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Author information

Authors and Affiliations

  1. Department of Mathematics, Statistics and Computer Science, St.Francis Xavier University, Antigonish, Canada

    Wendy MacCaull

  2. Department of Mathematical Logic, Sofia University, Sofia, Bulgaria

    Dimiter Vakarelov

Authors
  1. Wendy MacCaull
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  2. Dimiter Vakarelov
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Editor information

Editors and Affiliations

  1. Department of Mathematics, Statistics and Computer Science, St. Francis Xavier University, Antigonish, NS, Canada

    Wendy MacCaull

  2. Department of Computer Science, Brock University, L2S 3A1, St. Catharines, Ontario, Canada

    Michael Winter

  3. Computer Science Department, Brock University, L2S 3A1, St. Catharines, Ontario, Canada

    Ivo Düntsch

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© 2006 Springer-Verlag Berlin Heidelberg

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MacCaull, W., Vakarelov, D. (2006). Lattice-Based Paraconsistent Logic. In: MacCaull, W., Winter, M., Düntsch, I. (eds) Relational Methods in Computer Science. RelMiCS 2005. Lecture Notes in Computer Science, vol 3929. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11734673_14

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  • DOI: https://doi.org/10.1007/11734673_14

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-33339-5

  • Online ISBN: 978-3-540-33340-1

  • eBook Packages: Computer ScienceComputer Science (R0)

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