We propose a family of intuitionistic bilattices with full truth-knowledge duality (D-bilattices) for a logic programming. The first family of perfect D-bilattices is composed by Boolean algebras with even number of atoms: the simplest of them, based on intuitionistic truth-functionally complete extension of Belnap’s 4-valued bilattice, can be used in paraconsistent programming, that is, for knowledge bases with incomplete and inconsistent information. The other two families are useful for a probability theory where the uncertainty in the knowledge about a piece of information is in the form of belief types: as an interval (lower and upper boundary) probability or as a confidence level. Such programs can be parameterized by different kinds of probabilistic conjunctive/disjunctive strategies for their rules, based on intuitionistic implication. Such a framework offers a clear semantics for the satisfaction relation, and allows the extension of logic languages with intuitionistic implications also in the body of rules. From a theoretical point of view we introduce also a duality in higher-order bilatices, as in Temporal Probabilistic Logic, constructed as functional spaces over ordinary dual bilattices. Then we show the full truth-knowledge duality for a fixpoint semantics of logic programs based on dual bilattices. Finally we develop also an autoreferential version of Stone’s Representation Theorem for the dual bilattices. 1

Paraconsistent Logic Programs are a powerful mathematical formalism for dealing simultaneously with default, paraconsistent, and uncertainty reasoning forms. Disclosing recent results, we show how their semantics, Paraconsistent Well-Founded Models (WFMp), deal with inconsistent information and its propagation through program rules. In doing that we emphasize another key role the Coherence Principle plays in our semantics, and generalise results presented in [7]. By means of an illustrative example, we argue that not only should one extract paraconsistent conclusions when facing inconsistent information, but one may also obtain a precise clue as to which information depends on inconsistency.

Abstract. The adoption of standards by the knowledge representation and logic programming communities is essential for their visibility and impact. The Rule Interchange Format is a fundamental effort in this direction that should be supported by users, developers and theoreticians. For this reason, it is essential to the community to discuss the recommendations published by the W3C RIF Working Group. In particular, this paper presents the semantics of Rule Interchange Format (RIF) of multidocuments, analyses it and some deficiencies are elicited. A more general approach is proposed as an alternative semantics for multi-documents. As a side important result, some relevant problems in the semantics of RIF-FLD are also discussed and possible ways out are proposed.