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Nonmonotonic reasoning is sometimes simpler

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Computational Logic and Proof Theory (KGC 1993)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 713))

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Abstract

We establish the complexity of decision problems associated with the nonmonotonic modal logic S4. We prove that the problem of existence of an S4-expansion for a given set A of premises is Σ P2 -complete. Similarly, we show that for a given formula ϕ and a set A of premises, it is Σ P2 -complete to decide whether ϕ belongs to at least one S4-expansion for A, and it is Π P2 -complete to decide whether ϕ belongs to all S4-expansions for A. An interesting aspect of these results is that reasoning (testing satisfiability and provability) in the monotonic modal logic S4 is PSPACE-complete. To the best of our knowledge, the nonmonotonic logic S4 is the first example of a nonmonotonic formalism which is computationally easier than the monotonic logic that underlies it (assuming PSPACE does not collapse to Σ 2)P .

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Author information

Authors and Affiliations

  1. Robotics Laboratory, Computer Science Department, Stanford University, 94305, Stanford, CA, USA

    Grigori Schwarz

  2. Department of Computer Science, University of Kentucky, 40506, Lexington, KY, USA

    Miroslaw Truszczyński

Authors
  1. Grigori Schwarz
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  2. Miroslaw Truszczyński
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Georg Gottlob Alexander Leitsch Daniele Mundici

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© 1993 Springer-Verlag Berlin Heidelberg

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Schwarz, G., Truszczyński, M. (1993). Nonmonotonic reasoning is sometimes simpler. In: Gottlob, G., Leitsch, A., Mundici, D. (eds) Computational Logic and Proof Theory. KGC 1993. Lecture Notes in Computer Science, vol 713. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0022579

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  • DOI: https://doi.org/10.1007/BFb0022579

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-57184-1

  • Online ISBN: 978-3-540-47943-7

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