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Automated deduction with associative commutative operators

Michaël Rusinowitch 1 Laurent Vigneron 1
1 PROTHEO - Constraints, automatic deduction and software properties proofs
INRIA Lorraine, LORIA - Laboratoire Lorrain de Recherche en Informatique et ses Applications
Abstract : We propose a new inference system for automated deduction with equality and associative commutative operators. This system is an extension of the ordered paramodulation strategy. However, rather than using associativity and commutativity as the other axioms, they are handled by the AC-unification algorithm and the inference rules. Moreover, we prove the refutational completeness of this system without needing the functional reflexive axioms or AC-axioms. Such a result is obtained by semantic tree techniques. We also show that the inference system is compatible with simplification rules.
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https://hal.inria.fr/inria-00074775
Contributor : Rapport de Recherche Inria <>
Submitted on : Wednesday, May 24, 2006 - 4:17:12 PM
Last modification on : Friday, February 26, 2021 - 3:28:06 PM
Long-term archiving on: : Tuesday, April 12, 2011 - 7:19:45 PM

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  • HAL Id : inria-00074775, version 1

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Michaël Rusinowitch, Laurent Vigneron. Automated deduction with associative commutative operators. [Research Report] RR-1896, INRIA. 1993, pp.34. ⟨inria-00074775⟩

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