Resultants semantics for Prolog

In this paper we study some first-order formulas, called resultants, which can be used to describe in a concise way most of the relevant information associated to SLD-derivations. We first extend to resultants some classical results of logic programming theory. Then we define a fixpoint semantics for Prolog computed resultants, i.e. those formulas which are obtained by considering the leftmost selection rule. Suitable abstractions of such a semantics are then used to model call patterns and partial answers. Finally we show how these results can be generalized to a larger class of selection rules.