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Automated deduction with associative-commutative operators

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Applicable Algebra in Engineering, Communication and Computing Aims and scope

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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  1. CRIN and INRIA-Lorraine, BP239, 54506, Vandœuvre-lés-Nancy Cedex, France

    Michaël Rusinowitch & Laurent Vigneron

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  1. Michaël Rusinowitch
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  2. Laurent Vigneron
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Rusinowitch, M., Vigneron, L. Automated deduction with associative-commutative operators. AAECC 6, 23–56 (1995). https://doi.org/10.1007/BF01270929

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