Uncertainty and Partial Non-Uniform Assumptions in Parametric Deductive Databases

Different many-valued logic programming frameworks have been proposed to manage uncertain information in deductive databases and logic programming. A feature of these frameworks is that they rely on a predefined assumption or hypothesis, i.e. an interpretation that assigns the same default truth value to all the atoms of a program, e.g. in the open world assumption, by default all atoms have unknown truth value. In this paper we extend these frameworks along three directions: (i) we will introduce non-monotonic modes of negation; (ii) the default truth values of atoms need not necessarily to be all equal each other; and (iii) a hypothesis can be a partial interpretation. We will show that our approach extends the usual ones: if we restrict our attention to classical logic programs and consider total uniform hypotheses, then our semantics reduces to the usual semantics of logic programs. In particular, under the everything false assumption, our semantics captures and extends the well-founded semantics to these frameworks.