Static Semantics as Program Transformation and Well-founded Computation

In this paper, we propose a new constructive characterization of those semantics for disjunctive logic programs which are extensions of the well-founded semantics for normal programs. Based on considerations about how disjunctive information is treated by a given semantics, we divide the computation of that semantics into two phases. The first one is a program transformation phase, which applies axiom schemata expressing how derivations involving disjunctions are made in the given semantic framework. The second one is a constructive phase, based on a variation of the well-founded model construction for normal programs. We apply this two-phases procedural semantics to the computation of the static semantics of disjunctive logic programs as a case-study, showing how it works and what its results are in several examples. A main perspective of this proposal is a procedural semantics for disjunctive programs consisting of an inefficient preprocessing phase (implementing the program transformation procedure), to be however performed only once, and of an efficient runtime computation, obtained as a variation of any effective procedural semantics for the well-founded model.