A Compositional Proof Method of Partial Correctness for Normal Logic Programs with an application to Gödel

This report presents a new proof method of partial correctness for logic programs with negation based on a proof modularity. We prove in a compositional way that Fitting's or the well-founded semantics of the program is included in a specification. We give conditions for an abstract semantics to be compositional and we base our proof method on this property. We present also conservative but compositional extensions of Fitting's and of the well-founded semantics. As an illustration, an application is made to the module system of the Godel language. Moreover, our method is suitable for incremental validation since it does not require all parts of the program to be implemented. This document is an extended version of [9] which incorporates the missing proofs and a counter-example. R'esum'e Ce rapport pr'esente une nouvelle m'ethode de preuve de correction partielle pour des programmes logiques avec n'egation bas'ee sur des preuves modulaires. Nous montrons de fa¸con compositionelle que ..