The Model Evolution Calculus with Equality

  • Peter Baumgartner
  • Cesare Tinelli
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3632)

Abstract

In many theorem proving applications, a proper treatment of equational theories or equality is mandatory. In this paper we show how to integrate a modern treatment of equality in the Model Evolution calculus ( \(\mathcal{ME}\)), a first-order version of the propositional DPLL procedure. The new calculus, \(\mathcal{ME}_{\rm E}\), is a proper extension of the \(\mathcal{ME}\) calculus without equality. Like \(\mathcal{ME}\) it maintains an explicit candidate model, which is searched for by DPLL-style splitting. For equational reasoning \(\mathcal{ME}_{\rm E}\) uses an adapted version of the ordered paramodulation inference rule, where equations used for paramodulation are drawn (only) from the candidate model. The calculus also features a generic, semantically justified simplification rule which covers many simplification techniques known from superposition-style theorem proving. Our main result is the correctness of the \(\mathcal{ME}_{\rm E}\) calculus in the presence of very general redundancy elimination criteria.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Peter Baumgartner
    • 1
  • Cesare Tinelli
    • 2
  1. 1.Max-Planck Institute for Computer ScienceSaarbrücken
  2. 2.Department of Computer ScienceThe University of Iowa 

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