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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Horbach, M. (2010). Disunification for Ultimately Periodic Interpretations. In: Clarke, E.M., Voronkov, A. (eds) Logic for Programming, Artificial Intelligence, and Reasoning. LPAR 2010. Lecture Notes in Computer Science(), vol 6355. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-17511-4_17
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