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Routley Semantics for Answer Sets

  • Conference paper
Logic Programming and Nonmonotonic Reasoning (LPNMR 2005)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 3662))

Abstract

We present an alternative model theory for answer sets based on the possible worlds semantics proposed by Routley (1974) as a framework for the propositional logics of Fitch and Nelson. By introducing a falsity constant or second negation into Routley models, we show how paraconsistent as well as ordinary answer sets can be represented via a simple minimality condition on models. This means we can define a paraconsistent version of equilibrium logic, or paraconsistent answer sets (PAS) for propositional theories. The underlying logic of PAS is denoted by N 9. We characterise it axiomatically and algebraically, showing it to be the least conservative extension of the logic of here-and-there with strong negation. In addition, we show that N 9 captures the strong equivalence of programs in the paraconsistent case and can thus serve as a useful mathematical foundation for PAS. We end by showing that N 9 has the Interpolation Property.

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Author information

Authors and Affiliations

  1. Sobolev Institute of Mathematics, Novosobirsk, Russia

    Sergei Odintsov

  2. Universidad Rey Juan Carlos, Madrid, Spain

    David Pearce

Authors
  1. Sergei Odintsov
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  2. David Pearce
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Editor information

Editors and Affiliations

  1. School of Computing and Informatics, Arizona State University, 85287-8809, Tempe, AZ

    Chitta Baral

  2. Dipartimento di Matematica, Università della Calabria, I-87036, Rende, CS, Italy

    Gianluigi Greco  & Giorgio Terracina  & 

  3. Department of Mathematics, University of Calabria, 87036, Rende, CS, Italy

    Nicola Leone

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Odintsov, S., Pearce, D. (2005). Routley Semantics for Answer Sets. In: Baral, C., Greco, G., Leone, N., Terracina, G. (eds) Logic Programming and Nonmonotonic Reasoning. LPNMR 2005. Lecture Notes in Computer Science(), vol 3662. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11546207_27

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  • DOI: https://doi.org/10.1007/11546207_27

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-28538-0

  • Online ISBN: 978-3-540-31827-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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