On the Completeness of Arbitrary Selection Strategies for Paramodulation

  • Miquel Bofill
  • Guillem Godoy
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2076)

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].

Keywords

automated deduction 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Miquel Bofill
    • 1
  • Guillem Godoy
    • 2
  1. 1.Dept. IMAUniversitat de GironaGironaSpain
  2. 2.Dept. LSITechnical University of CataloniaBarcelonaSpain

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