We report our research on semantics for normal/disjunctive programs. One of the most well known semantics for logic programming is the stable semantics (STABLE). However, it is well known that very often STABLE has no models. In this paper we study the stable semantics and present some new results about it. Furthermore, we introduce a new semantics (that we call D3-WFS-DCOMP) and compare it with STABLE. For normal programs, this semantics is based on a suitable integration of 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 non minimal model or a non minimal 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 transformations accepted by STABLE. We also introduce a 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 a third new semantics that insists in the use of implicit disjunctions. We briefly sketch how these semantics can be extended to programs including: explicit negation, default negation in the head of a clause, as well as a lub operator ( which is the generalization of setof over arbitrary complete lattices). We sketch how to model this lub operator using standard disjunctive clauses. However, we can not use the STABLE semantics but instead any of our suggested semantics. We emphasizes that the ultimate goal of our research is to understand better the STABLE semantics and to suggest solutions to the drawbacks of the stable semantics (that becomes undefined very often).