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Déduction et Unification dans les Théories Permutatives

Abstract : There exist several theorem provers that perform deduction modulo an equational theory, i.e. by considering equivalence classes of terms, instead of ordinary terms. In general, most of the research carried out in this area focuses on determining new techniques to perform deduction modulo one particular theory. In [Avenhaus & Plaisted, 2001], Jürgen Avenhaus and David Plaisted sought for new techniques that could be used for the treatment of not one particular theory, but an entire class of equational theories: the so-called permutative theories. The authors introduced the notions of stratified terms and stratified sets, and described the procedures that should be implemented in a theorem prover based on stratified terms. Permutative theories enjoy several regularity properties that make it possible to use efficient techniques from computational group theory to deal with them. The authors hoped that the efficiency of these techniques would counterbalance the high number of clauses that could be generated by a theorem prover based on stratified terms. However, the algorithms they propose to perform deduction on stratified terms are based on an explicit enumeration of the elements of a group, and are therefore exponential. In this thesis, we develop Avenhaus and Plaisted’s work, and adapt their formalism to make a more intensive use of group-theoretic tools.
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Contributor : Mnacho Echenim <>
Submitted on : Monday, December 19, 2005 - 12:47:33 PM
Last modification on : Friday, November 6, 2020 - 3:45:01 AM
Long-term archiving on: : Saturday, April 3, 2010 - 7:37:08 PM


  • HAL Id : tel-00011236, version 1




Mnacho Echenim. Déduction et Unification dans les Théories Permutatives. Autre [cs.OH]. Institut National Polytechnique de Grenoble - INPG, 2005. Français. ⟨tel-00011236⟩



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