Summary: 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 specialized to normal programs. Our framework consists of two parts: (a) a semantical, where semantics are defined in an abstract way as the weakest semantics satisfying certain properties, and (b) a procedural, namely a bottom-up query evaluation method based on operators working on conditional facts. As to (a), we concentrate in this paper on a particular set of abstract properties (the most important being the unfolding or partial evaluation property GPPE) and define a new semantics D-WFS, which extends WFS and GCWA. We also mention that various other semantics, like Fitting's \(\text{comp}_3\), Schlipf's \(\text{WFS}_C\), Gelfond and Lifschitz' STABLE and Ross and Topor's WGCWA [also introduced independently by \textit{A. Rajasekar}, \textit{J. Lobo} and \textit{J. Minker}, J. Autom. Reasoning 5, No. 3, 293-307 (1989; Zbl 0683.68086)], can be captured in our framework. In (b) we compute for any program \(P\) a residual program \(\text{res}(P)\), and show that \(\text{res}(P)\) 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, \(\text{res}(P)\) is complete for D-WFS, WFS and GCWA.