**Default Knowledge in Logic Programs with Uncertainty**

In Proceedings of the 19th International Conference on Logic Programming (ICLP-2003).

**Abstract: **Many frameworks have been proposed to manage uncertain information in logic programming. Essentially, they differ in the underlying notion of uncertainty and how these uncertainty values, associated to rules and facts, are managed. The goal of this paper is to allow the reasoning with non-uniform default assumptions, ie. with any arbitrary assignment of default values to the atoms. Informally, rather than to rely on the same default value for all atoms, we allow arbitrary assignments of default certainty values to complete the available information. To this end, we define both epistemologically and computationally the semantics according to any given assumption. For reasons of generality, we present our work in the framework presented in~\cite{Lakshmanan01} as a unifying umbrella for many of the proposed approaches to the management of uncertainty in logic programming. Our extension is conservative in the following sense: (i) if we restrict our attention to the usual uniform Open World Assumption (by default all atoms have unknown truth-value), then the semantics reduces to the Kripke-Kleene semantics, and (ii) if we restrict our attention to the uniform Closed World Assumption (all atoms are false by default), then our semantics reduces to the well-founded semantics.