Hypothesis-based semantics of logic programs in multivalued logics

Authors:
Yann Loyer;Nicolas Spyratos;Daniel Stamate
Affiliations:
Université de Versailles-Saint-Quentin-en-Yvelines, Versailles, France;Universitél de Paris Sud---Orsay, Orsay, France;University of London, London, U.K.
Venue:
ACM Transactions on Computational Logic (TOCL)
Year:
2004

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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.