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Disunification for Ultimately Periodic Interpretations

  • Matthias Horbach
Conference paper
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.

Keywords

Normal Form Function Symbol Horn Clause Equational Formula Periodic Decomposition 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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