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Finding Finite Herbrand Models

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Logic for Programming, Artificial Intelligence, and Reasoning (LPAR 2012)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7180))

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Abstract

We show that finding finite Herbrand models for a restricted class of first-order clauses is ExpTime-complete. A Herbrand model is called finite if it interprets all predicates by finite subsets of the Herbrand universe. The restricted class of clauses consists of anti-Horn clauses with monadic predicates and terms constructed over unary function symbols and constants. The decision procedure can be used as a new goal-oriented algorithm to solve linear language equations and unification problems in the description logic \(\mathcal{FL}_0\). The new algorithm has only worst-case exponential runtime, in contrast to the previous one which was even best-case exponential.

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Author information

Authors and Affiliations

  1. Theoretical Computer Science, TU Dresden, Germany

    Stefan Borgwardt & Barbara Morawska

Authors
  1. Stefan Borgwardt
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  2. Barbara Morawska
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Editors and Affiliations

  1. Microsoft Research, One Microsoft Way, 98052-6399, Redmond, WA, USA

    Nikolaj Bjørner

  2. School of computer Science, University of Manchester, Kilburn Building, Oxford Road, MP13 9PL, Manchester, UK

    Andrei Voronkov

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Borgwardt, S., Morawska, B. (2012). Finding Finite Herbrand Models. In: Bjørner, N., Voronkov, A. (eds) Logic for Programming, Artificial Intelligence, and Reasoning. LPAR 2012. Lecture Notes in Computer Science, vol 7180. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-28717-6_13

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  • DOI: https://doi.org/10.1007/978-3-642-28717-6_13

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-28716-9

  • Online ISBN: 978-3-642-28717-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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