Semantics of (disjunctive) logic programs based on partial evaluation
The Journal of Logic Programming
We present a new and general approach for defining, understanding, and computing logic programming semantics. We consider disjunctive programs for generality, but our results are still interesting if speciahzed to normal programs. Our framework consists of two parts: (a) a semantical, where semantics are defined iu an abstract wz~y as the weakest semantics satisfying certain properties, arid (bJ a procedural, namely a bottom-up query evaluation method based on operators working on conditional
... cts. As to (a), we concentrate in this paper on a particular set of abstract properties (the most important being the unfolding or partial eraluation property GPPE) and define a new sema,atics D-WFS, which extends WFS and GCWA. We also mention that various other semantics, like FittinT's romp3, Schlipf's WFSc, Gelfond and Lifschitz" STABLE and Ross and Topor's WGCWA (also introduced independently by Rajasekar et aI. (A. Rajasekar, J. Lobo, J. Minker, Journal of Automated Reasoning 5 (1989) 293-307)), can be captured in our framework. In (b)we compute for any program P a residual program res(P), and show that res(P) is equivalent to the original program under very general conditions on the semantics (which are satisfied, e.g., by the well-founded, stable, stationary, and static semantics). Many queries with respect to these semantics can already be answered on the basis of the residual program. In fact, res(P) is complete for D-WFS, WFS and GCWA.