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International Workshop on Computer Science Logic

CSL 2009: Computer Science Logic pp 332–347Cite as

Deciding the Inductive Validity of ∀ ∃ * Queries

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5771))

Abstract

We present a new saturation-based decidability result for inductive validity. Let \(\it \Sigma\) be a finite signature in which all function symbols are at most unary and let N be a satisfiable Horn clause set without equality in which all positive literals are linear. If N ∪ {A 1,...,A n →} belongs to a class that can be finitely saturated by ordered resolution modulo variants, then it is decidable whether a sentence of the form \(\forall x.\exists\vec y.A_1\wedge\ldots\wedge A_n\) is valid in the minimal model of N.

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Author information

Authors and Affiliations

  1. Max Planck Institute for Informatics, Saarbrücken, Germany

    Matthias Horbach & Christoph Weidenbach

Authors
  1. Matthias Horbach
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  2. Christoph Weidenbach
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Editor information

Editors and Affiliations

  1. Mathematische Grundlagen der Informatik, RWTH Aachen, 52056, Aachen, Germany

    Erich Grädel

  2. CENTRIA and Departamento de Matemática, Universidade Nova de Lisboa, 2829-516, Caparica, Portugal

    Reinhard Kahle

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Horbach, M., Weidenbach, C. (2009). Deciding the Inductive Validity of ∀ ∃ * Queries. In: Grädel, E., Kahle, R. (eds) Computer Science Logic. CSL 2009. Lecture Notes in Computer Science, vol 5771. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04027-6_25

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  • DOI: https://doi.org/10.1007/978-3-642-04027-6_25

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-04026-9

  • Online ISBN: 978-3-642-04027-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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