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Article Dans Une Revue Journal of Automated Reasoning Année : 2007

Structures for abstract rewriting

Résumé

When rewriting is used to generate convergent and complete rewrite systems in order to answer the validity problem for some theories, all the rewriting theories rely on a same set of notions, properties and methods. Rewriting techniques have mainly been used to answer the validity problem of equational theories, that is to compute congruences. However, recently, they have been extended in order to be applied to other algebraic structures such as pre-orders and orders. In this paper, we investigate an abstract form of rewriting, by following the paradigm of ``logical-system independency''. To achieve this purpose, we provide a few simple conditions (or axioms) under which rewriting (and then the set of classical properties and methods) can be modeled, understood, studied, proven and generalized. This enables us to extend rewriting techniques to other algebraic structures than congruences and pre-orders such as congruences closed under monotonicity and modus-ponens. Finally, we introduce convergent rewrite systems that enable one to describe deduction procedures for their corresponding theory, and propose a Knuth-Bendix style completion procedure in this abstract framework.
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Dates et versions

hal-00341965 , version 1 (19-07-2009)

Identifiants

Citer

Marc Aiguier, Diane Bahrami. Structures for abstract rewriting. Journal of Automated Reasoning, 2007, 38, pp.303--351. ⟨10.1007/s10817-006-9065-7⟩. ⟨hal-00341965⟩
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