Extending Well-Founded Semantics with Clark’s Completion for Disjunctive Logic Programs

In this paper, we introduce new semantics (that we call D3-WFS-DCOMP) and compare it with the stable semantics (STABLE). For normal programs, this semantics is based on suitable integration of the well-founded semantics (WFS) and the Clark’s completion. D3-WFS-DCOM has the following appealing properties: First, it agrees with STABLE in the sense that it never defines a nonminimal model or a nonminimal supported model. Second, for normal programs it extends WFS. Third, every stable model of a disjunctive program P is a D3-WFS-DCOM model of P. Fourth, it is constructed using transformation rules accepted by STABLE. We also introduce second semantics that we call D2-WFS-DCOMP. We show that D2-WFS-DCOMP is equivalent to D3-WFS-DCOMP for normal programs but this is not the case for disjunctive programs. We also introduce third new semantics that supports the use of implicit disjunctions. We illustrate how these semantics can be extended to programs including explicit negation, default negation in the head of a clause, and a lub operator, which is a generalization of the aggregation operator setof over arbitrary complete lattices