Paraconsistent Reasoning via Quantified Boolean Formulas, II: Circumscribing Inconsistent Theories

  • Philippe Besnard
  • Torsten Schaub
  • Hans Tompits
  • Stefan Woltran
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2711)


Through minimal-model semantics, three-valued logics provide an interesting formalism for capturing reasoning from inconsistent information. However, the resulting paraconsistent logics lack so far a uniform implementation platform. Here, we address this and specifically provide a translation of two such paraconsistent logics into the language of quantified Boolean formulas (QBFs). These formulas can then be evaluated by off-the-shelf QBF solvers. In this way, we benefit from the following advantages: First, our approach allows us to harness the performance of existing QBF solvers. Second, different paraconsistent logics can be compared with in a unified setting via the translations used. We alternatively provide a translation of these two paraconsistent logics into quantified Boolean formulas representing circumscription, the well-known system for logical minimization. All this forms a case study inasmuch as the other existing minimization-based many-valued paraconsistent logics can be dealt with in a similar fashion.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Philippe Besnard
    • 1
  • Torsten Schaub
    • 2
  • Hans Tompits
    • 3
  • Stefan Woltran
    • 3
  1. 1.IRIT-CNRSToulouse CedexFrance
  2. 2.Institut für InformatikUniversität PotsdamPotsdamGermany
  3. 3.Institut für Informationssysteme 184/3Technische Universität WienViennaAustria

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