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Schémas de formules et de preuves en logique propositionnelle

Vincent Aravantinos 1
1 CAPP - Calculs algorithmes programmes et preuves
LIG - Laboratoire d'Informatique de Grenoble
Abstract : This thesis lies in the field of automated deduction, i.e. the development of algorithms aiming at proving automatically some mathematical conjectures. In this thesis, the conjectures that we want to prove belong to an extension of propositional logic called ``formula schemas''. Those objects allow to represent infinitely many propositional formulae in a finite way (similarly to the way that regular languages finitely represent infinitely many words). Proving a formula schema amounts to prove (at once) all the formulae that it represents. We show that the problem of proving formula schemas is undecidable in general. The remaining part of the thesis presents algorithms that still try to prove schemas (event though, of course, they do not terminate in general). Those algorithms allow to identify decidable classes of schemas, i.e. classes for which there exists an algorithm that always terminates for any entry by answering if the schema is valid or not. One of those algorithms have been implemented. Proof methods that are presented here mix classical procedures for propositional logic (DPLL or semantic tableaux) and inductive reasoning. Inductive reasoning is achieved by the use of ``cyclic proofs'', i.e. infinite proofs in which cycles are automatically detected. In such a case, we can turn those infinite proofs into finite objects, which we can call ``proofs schemas''.
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https://tel.archives-ouvertes.fr/tel-00523658
Contributor : Vincent Aravantinos <>
Submitted on : Wednesday, October 6, 2010 - 8:37:26 AM
Last modification on : Monday, April 20, 2020 - 11:16:02 AM
Document(s) archivé(s) le : Thursday, October 25, 2012 - 4:31:17 PM

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Vincent Aravantinos. Schémas de formules et de preuves en logique propositionnelle. Autre [cs.OH]. Institut National Polytechnique de Grenoble - INPG, 2010. Français. ⟨tel-00523658⟩

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