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E-unification en demonstration automatique

Abstract : Since Martelli and Montanari's work in 1982, E-unification problems are often considered are set of equations. This thesis presents new transformation rules which describe application of axioms at the root of the terms. The theoretical properties are established (soundness, completeness, ...). We also prove that this approach, based on strictly resolvent presentations, is more general than well known algorithms (Root-Rewriting [J. Gallier & W. Snyder], Syntactic mutation [C. Kirchner]). The analysis of the behavior of these rules proves the interest of the applica- tion of axioms at the root and suggests which strictly resolvent presentations should give the best results. These presentations are generated automatically. The theoreti- cal properties of the given completion rules are proved thanks to the notion of strictly resolvent completion. Different strategies are studied, going from a terminating strategy to a (potentially divergent) strategy resulting in very efficient presentations. Theoretical researches can be done in this (new) general frame- work. They apply to the subsumed algorithms. For instance, paral- lelism is studied and leads to a compact presentation of the com- puted unifiers. Other more complex optimisations are also stu- died. The detection of useless instanciations while unifying with the left hand-side of a rule is the most important. It is useful to prove the completeness of the solution found for a given prob- lem when the presentation is not strictly resolvent (divergent completion). Experimental results show the simplicity and the generality of this new approach. Its generality allows comparison with other well-known algorithms and justifies the usefulness of the diver- gent strategy. The study of particular cases proves that it leads to very interesting results in a reasonable time. Thus, this E- unification procedure can be used in a theorem prover.
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https://tel.archives-ouvertes.fr/tel-00005085
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Submitted on : Wednesday, February 25, 2004 - 11:35:37 AM
Last modification on : Friday, November 6, 2020 - 4:39:29 AM
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  • HAL Id : tel-00005085, version 1

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Bertrand Delsart. E-unification en demonstration automatique. Interface homme-machine [cs.HC]. Institut National Polytechnique de Grenoble - INPG, 1994. Français. ⟨tel-00005085⟩

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