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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References
Bachmair, L., Ganzinger, H.: Equational Reasoning in Saturation-Based Theorem Proving. In: Bibel, W., Schmitt, P.H. (eds.) Automated Deduction. A Basis for Applications, Foundations. Calculi and Refinements, vol. I, pp. 353–398. Kluwer, Dordrecht (1998)
Baumgartner, P.: FDPLL – A First-Order Davis-Putnam-Logeman-Loveland Procedure. In: McAllester, D. (ed.) CADE 2000. LNCS, vol. 1831, pp. 200–219. Springer, Heidelberg (2000)
Baumgartner, P., Fuchs, A., Tinelli, C.: Implementing the Model Evolution Calculus. In: International Journal on Artificial Intelligence Tools, IJAIT (2005) (to appear)
Baumgartner, P., Tinelli, C.: The model evolution calculus. In: Baader, F. (ed.) CADE 2003. LNCS (LNAI), vol. 2741, pp. 350–364. Springer, Heidelberg (2003)
Baumgartner, P., Tinelli, C.: The Model Evolution Calculus with Equality (2005), http://www.mpi-sb.mpg.de/~baumgart/publications/MEE.pdf
Billon, J.-P.: The Disconnection Method. In: Miglioli, P., Moscato, U., Ornaghi, M., Mundici, D. (eds.) TABLEAUX 1996. LNCS, vol. 1071, pp. 110–126. Springer, Heidelberg (1996)
Davis, M., Logemann, G., Loveland, D.: A Machine Program for Theorem Proving. Communications of the ACM 5(7), 394–397 (1962)
Ganzinger, H., Korovin, K.: Integrating equational reasoning into instantiation-based theorem proving. In: Marcinkowski, J., Tarlecki, A. (eds.) CSL 2004. LNCS, vol. 3210, pp. 71–84. Springer, Heidelberg (2004)
Ganzinger, H., Korovin, K.: New Directions in Instance-Based Theorem Proving. In: Proc. LICS (2003)
Letz, R., Stenz, G.: Integration of equality reasoning into the disconnection calculus. In: Egly, U., Fermüller, C. (eds.) TABLEAUX 2002. LNCS (LNAI), vol. 2381, pp. 176–190. Springer, Heidelberg (2002)
Nieuwenhuis, R., Rubio, A.: Paramodulation-Based Theorem Proving. In: Robinson, J.A., Voronkov, A. (eds.) Handbook of Automated Reasoning, pp. 371–443. Elsevier, Amsterdam (2001)
Plaisted, D.A., Zhu, Y.: Ordered Semantic Hyper Linking. Journal of Automated Reasoning 25(3), 167–217 (2000)
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Baumgartner, P., Tinelli, C. (2005). The Model Evolution Calculus with Equality. In: Nieuwenhuis, R. (eds) Automated Deduction – CADE-20. CADE 2005. Lecture Notes in Computer Science(), vol 3632. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11532231_29
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DOI: https://doi.org/10.1007/11532231_29
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