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A Paraconsistent Higher Order Logic

  • Conference paper
Artificial Intelligence and Symbolic Computation (AISC 2004)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 3249))

Abstract

Classical logic predicts that everything (thus nothing useful at all) follows from inconsistency. A paraconsistent logic is a logic where an inconsistency does not lead to such an explosion, and since in practice consistency is difficult to achieve there are many potential applications of paraconsistent logics in knowledge-based systems, logical semantics of natural language, etc.

Higher order logics have the advantages of being expressive and with several automated theorem provers available. Also the type system can be helpful.

We present a concise description of a paraconsistent higher order logic with countably infinite indeterminacy, where each basic formula can get its own indeterminate truth value. The meaning of the logical operators is new and rather different from traditional many-valued logics as well as from logics based on bilattices. Thus we try to build a bridge between the communities of higher order logic and many-valued logic.

A case study is studied and a sequent calculus is proposed based on recent work by Muskens.

This research was partly sponsored by the IT University of Copenhagen.

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Author information

Authors and Affiliations

  1. Computer Science, Roskilde University, Building 42.1, DK-4000, Roskilde, Denmark

    Jørgen Villadsen

Authors
  1. Jørgen Villadsen
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Editor information

Editors and Affiliations

  1. Research Institute for Symbolic Computation, Johannes Kepler University, Linz, Austria

    Bruno Buchberger

  2. Department of Computer Science, University College London, Gower Street, WC1E 6BT, London, UK

    John Campbell

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Villadsen, J. (2004). A Paraconsistent Higher Order Logic. In: Buchberger, B., Campbell, J. (eds) Artificial Intelligence and Symbolic Computation. AISC 2004. Lecture Notes in Computer Science(), vol 3249. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30210-0_5

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  • DOI: https://doi.org/10.1007/978-3-540-30210-0_5

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-23212-4

  • Online ISBN: 978-3-540-30210-0

  • eBook Packages: Springer Book Archive

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