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Conference Papers Year : 2003

## Predicate Synthesis from Inductive Proof Attempt of Faulty Conjectures

Francis Alexandre
• Function : Author
• PersonId : 830098

#### Abstract

We present a method for patching faulty conjectures in automatic theorem proving. 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.

Other [cs.OH]

### Dates and versions

inria-00100052 , version 1 (26-09-2006)

### Identifiers

• HAL Id : inria-00100052 , version 1

### Cite

Francis Alexandre, Khaled Bsaïes, Moussa Demba. Predicate Synthesis from Inductive Proof Attempt of Faulty Conjectures. Logic Based Program Synthesis and Transformation: 13th International Symposium - LOPSTR 2003, Maurice Bruynooghe, 2003, Uppsala, Sweden, pp.20-33. ⟨inria-00100052⟩

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