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On the Completeness of Arbitrary Selection Strategies for Paramodulation

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Automata, Languages and Programming (ICALP 2001)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2076))

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Abstract

A crucial way for reducing the search space in automated deduction are the so-called selection strategies: in each clause, the subset of selected literals are the only ones involved in inferences.

For first-order Horn clauses without equality, resolution is complete with an arbitrary selection of one single literal in each clause [dN96].

For Horn clauses with built-in equality, i.e., paramodulation-based inference systems, the situation is far more complex. Here we show that if a paramodulation-based inference system is complete with eager selection of negative equations and, moreover, it is compatible with equality constraint inheritance, then it is complete with arbitrary selection strategies. A first important application of this result is the one for paramodulation wrt. non-monotonic orderings, which was left open in [BGNR99].

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Author information

Authors and Affiliations

  1. Dept. IMA, Universitat de Girona, Lluís Santaló s/n, 17071, Girona, Spain

    Miquel Bofill

  2. Dept. LSI, Technical University of Catalonia, Jordi Girona 1, 08034, Barcelona, Spain

    Guillem Godoy

Authors
  1. Miquel Bofill
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  2. Guillem Godoy
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Editor information

Editors and Affiliations

  1. Departament de Llenguatges i Sistemes Informátics, Univ. Politècnica de Catalunya, C/Jordi Girona Salgado 1-3, 08034, Barcelona, Spain

    Fernando Orejas

  2. Computer Technology Institute (CTI), University of Patras, 61 Riga Feraiou street, 26221, Patras, Greece

    Paul G. Spirakis

  3. Institute of Information and Computing Sciences, Utrecht University, Padualaan 14, 3584, CH, Utrecht, The Netherlands

    Jan van Leeuwen

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© 2001 Springer-Verlag Berlin Heidelberg

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Bofill, M., Godoy, G. (2001). On the Completeness of Arbitrary Selection Strategies for Paramodulation. In: Orejas, F., Spirakis, P.G., van Leeuwen, J. (eds) Automata, Languages and Programming. ICALP 2001. Lecture Notes in Computer Science, vol 2076. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48224-5_77

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  • DOI: https://doi.org/10.1007/3-540-48224-5_77

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-42287-7

  • Online ISBN: 978-3-540-48224-6

  • eBook Packages: Springer Book Archive

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