Disunification for Ultimately Periodic Interpretations

  • Matthias Horbach
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6355)

Abstract

Disunification is an extension of unification to first-order formulae over syntactic equality atoms. Instead of considering only syntactic equality, I extend a disunification algorithm by Comon and Delor to ultimately periodic interpretations, i.e. minimal many-sorted Herbrand models of predicative Horn clauses and, for some sorts, equations of the form s l (x) ≃ s k (x). The extended algorithm is terminating and correct for ultimately periodic interpretations over a finite signature and gives rise to a decision procedure for the satisfiability of equational formulae in ultimately periodic interpretations.

As an application, I show how to apply disunification to compute the completion of predicates with respect to an ultimately periodic interpretation. Such completions are a key ingredient to several inductionless induction methods.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Matthias Horbach
    • 1
    • 2
  1. 1.Max-Planck-Institut für InformatikSaarbrückenGermany
  2. 2.Saarland UniversitySaarbrückenGermany

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