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Paraconsistent Reasoning via Quantified Boolean Formulas, I: Axiomatising Signed Systems

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Logics in Artificial Intelligence (JELIA 2002)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 2424))

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Abstract.

Signed systems were introduced as a general, syntax-independent framework for paraconsistent reasoning, that is, non-trivialised reasoning from inconsistent information. In this paper, we show how the family of corresponding paraconsistent consequence relations can be axiomatised by means of quantified Boolean formulas. This approach has several benefits. First, it furnishes an axiomatic specification of paraconsistent reasoning within the framework of signed systems. Second, this axiomatisation allows us to identify upper bounds for the complexity of the different signed consequence relations. We strengthen these upper bounds by providing strict complexity results for the considered reasoning tasks. Finally, we obtain an implementation of different forms of paraconsistent reasoning by appeal to the existing system QUIP.

The work was partially supported by the Austrian Science Foundation under grant P15068.

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Author information

Authors and Affiliations

  1. Institut für Informatik, Universität Potsdam, Postfach 90 03 27, D-14439, Potsdam, Germany

    Philippe Besnard & Torsten Schaub

  2. Institut für Informationssysteme 184/3, Technische UniversitätWien, Favoritenstraße 9-11, A-1040, Vienna, Austria

    Hans Tompits & Stefan Woltran

Authors
  1. Philippe Besnard
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  2. Torsten Schaub
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  3. Hans Tompits
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  4. Stefan Woltran
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Editor information

Editors and Affiliations

  1. DEIS, University of Calabria, P.te P. Bucci, Cubo 41C, 87036, Rende, CS, Italy

    Sergio Flesca  & Sergio Greco  & 

  2. Department of Mathematics, University of Calabria, P.te P. Bucci, Cubo 30B, 87036, Rende, CS, Italy

    Giovambattista Ianni  & Nicola Leone  & 

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© 2002 Springer-Verlag Berlin Heidelberg

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Besnard, P., Schaub, T., Tompits, H., Woltran, S. (2002). Paraconsistent Reasoning via Quantified Boolean Formulas, I: Axiomatising Signed Systems. In: Flesca, S., Greco, S., Ianni, G., Leone, N. (eds) Logics in Artificial Intelligence. JELIA 2002. Lecture Notes in Computer Science(), vol 2424. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45757-7_27

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  • DOI: https://doi.org/10.1007/3-540-45757-7_27

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-44190-8

  • Online ISBN: 978-3-540-45757-2

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