The well-founded semantics in normal logic programs with uncertainty

Many frameworks of logic programming have been proposed to manage uncertain information in deductive databases and expert systems. Roughly, on the basis of how uncertainty is associated to facts and the rules in a program, they can be classified into implication-based (IB) and annotation-based (AB). However, one fundamental issue that remains unaddressed in the IB approach is the representation and the manipulation of the non-monotonic mode of negation, an important feature for real applications. Our focus in this paper is to introduce non-monotonic negation in the parametric IB framework, a unifying umbrella for IB frameworks. The semantical approach that we will adopt is based on the well-founded semantics, one of the most widely studied and used semantics of (classical) logic programs with negation.