# A Method for Patching Faulty Conjectures

2 DEDALE - Development of specifications
LORIA - Laboratoire Lorrain de Recherche en Informatique et ses Applications
Abstract : We present a method for patching faulty conjectures in automatic theorem proving. The method is based on well-known folding/unfolding deduction rules. The conjectures we are interested in here are implicative formulas that are of the following form\,: $\forall \overline{ x}~\phi( \overline{ x})=\forall \overline{x} ~\exists \overline{Y} ~\Gamma(\overline{x},\overline{Y}) \leftarrow \Delta(\overline{x})$. A faulty conjecture is a statement $\forall \overline{ x}~\phi( \overline{ x})$, which is not provable in some given program ${\cal T}$, defining all the predicates occurring in $\phi$, i.e, ${\cal M(T)}\not \models \forall \overline{ x}~ \phi( \overline{ x})$, where ${\cal M(T)}$ means the least Herbrand model of ${\cal T}$, but it would be if enough conditions, say $P$, were assumed to hold, i.e., ${\cal M(T\cup P)}\models \forall \overline{ x}~ \phi( \overline{ x})\leftarrow P$, where ${\cal P}$ is the definition of $P$. The missing hypothesis $P$ is called a corrective predicate for $\phi$. To construct $P$, we use the abduction mechanism that is the process of hypothesis formation. In this paper, we use the logic based approach because it is suitable for the application of deductive rules.
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Rapport
[Intern report] A04-R-321 || demba04a, 2004, 20 p
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https://hal.inria.fr/inria-00100226
Contributeur : Publications Loria <>
Soumis le : mardi 26 septembre 2006 - 10:15:45
Dernière modification le : mardi 24 avril 2018 - 13:36:45

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• HAL Id : inria-00100226, version 1

### Citation

Moussa Demba, Francis Alexandre, Khaled Bsaïes. A Method for Patching Faulty Conjectures. [Intern report] A04-R-321 || demba04a, 2004, 20 p. 〈inria-00100226〉

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