Hypothesis-based semantics of logic programs in multivalued logics

Abstract

We address the problem of defining semantics for logic programs in presence of incomplete and contradictory information coming from different sources. The information consists of facts that a central server collects and tries to combine using (a) a set of logical rules, that is, a logic program, and (b) a hypothesis representing the server's own estimates. In such a setting incomplete information from a source or contradictory information from different sources necessitate the use of many-valued logics in which programs can be evaluated and hypotheses can be tested. To carry out such activities we propose a formal framework based on bilattices such as Belnap's four-valued logics. In this framework we work with the class of programs defined by Fitting and we propose hypothesis-based semantics for such programs. We also establish an intuitively appealing connection between our hypothesis testing mechanism, on the one hand, and the well-founded semantics and Kripke-Kleene semantics of Datalog programs with negation, on the other hand.