The Approximate Well-founded Semantics for Logic Programs with Uncertainty

The management of uncertain information in logic programs becomes to be important whenever the real world information to be represented is of imperfect nature and the classical crisp {em true, false} approximation is not adequate. A general framework, called emph{Parametric Deductive Databases with Uncertainty} (PDDU) framework~cite{Lakshmanan01}, was proposed as a unifying umbrella for many existing approaches towards the manipulation of uncertainty in logic programs. We extend PDDU with (non-monotonic) negation, a well-known and important feature of logic programs. We show that, dealing with uncertain and incomplete knowledge, atoms should be assigned only approximations of uncertainty values, unless some assumption is used to complete the knowledge. We rely on the closed world assumption to infer as much default ``false'' knowledge as possible. Our approach leads also to a novel characterizations, both epistemic and operational, of the well-founded semantics in PDDU, and preserves the continuity of the immediate consequence operator, a major feature of the classical PDDU framework.