Intuitionistic Implication and Resolution

Some recent works rely on the intuitionistic theory of Hereditary Harrop formulas to provide extensions for Horn clauses while preserving the logic paradigm. In particular, an intuitionistic implication is used to provide some form of scoping. However the lack of appropriate evaluation strategies, notably a strategy relying on a forward-chaining search, has limited its application. This paper investigates a resolution schema for propositional Hereditary Harrop formulas, extending the resolution for Horn Clauses. A particular restriction of this resolution schema provides a speciication of bottom-up search in presence of embedded intuitionistic implications. A decidable bottom-up procedure is given by a further reenement.