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International Workshop on Theorem Proving with Analytic Tableaux and Related Methods

TABLEAUX 1996: Theorem Proving with Analytic Tableaux and Related Methods pp 278–294Cite as

A tableau calculus for minimal model reasoning

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Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 1071))

Abstract

The paper studies the automation of minimal model inference, i.e., determining whether a formula is true in every minimal model of the premises. A novel tableau calculus for prepositional minimal model reasoning is presented in two steps. First an analytic clausal tableau calculus employing a restricted cut rule is introduced. Then the calculus is extended to handle minimal model inference by employing a groundedness property of minimal models. A decision procedure based on the basic calculus is devised and then it is extended to minimal model inference. The basic decision procedure and its extension enjoy some interesting properties. When deciding logical consequence, the basic procedure explores the search space of counter-models with a preference to minimal models and each counter-model is not generated more than once. The procedures can be implemented to run in polynomial space, and they provide polynomial time decision procedures for Horn clauses. The extended decision procedure can also be used to finding all minimal models of a set of clauses.

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Authors and Affiliations

  1. Dept. of Computer Science, University of Koblenz, Rheinau 1, D-56075, Koblenz, Germany

    Ilkka Niemelä

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  1. Ilkka Niemelä
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Editor information

P. Miglioli U. Moscato D. Mundici M. Ornaghi

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© 1996 Springer-Verlag Berlin Heidelberg

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Niemelä, I. (1996). A tableau calculus for minimal model reasoning. In: Miglioli, P., Moscato, U., Mundici, D., Ornaghi, M. (eds) Theorem Proving with Analytic Tableaux and Related Methods. TABLEAUX 1996. Lecture Notes in Computer Science, vol 1071. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-61208-4_18

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  • DOI: https://doi.org/10.1007/3-540-61208-4_18

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-61208-7

  • Online ISBN: 978-3-540-68368-1

  • eBook Packages: Springer Book Archive

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