The model evolution calculus with equality

  • Authors:

  • Peter Baumgartner;Cesare Tinelli

  • Affiliations:

  • Max-Planck Institute for Computer Science, Saarbrücken;Department of Computer Science, The University of Iowa

  • Venue:
  • CADE' 20 Proceedings of the 20th international conference on Automated Deduction
  • Year:
  • 2005

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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.