Hypotheses Founded Semantics of Logic Programs for Information Integration in Multi-Valued Logics

We address the problem of integrating 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, i.e. 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 develop a theory for information integration. 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.