Abstract of Paper

The Approximate Well-founded Semantics for Logic Programs with Uncertainty
by Yann Loyer and Umberto Straccia

Abstract:

The management of uncertain information in logic programs and deductive
databases becomes to be important whenever the real world information to be
represented is of imperfect nature and the classical crisp true, false
approximation is not adequate. A general framework, called Parametric
Deductive Databases with Uncertainty (PDDU) framework [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.