Assumption based multi-valued semantics for extended logic programs

The paper presents an approach for handling uncertain information in extended logic programs using multi-valued logics defined by bilattices. Uncertainty means that the atoms may be assigned logical values other than the conventional ones - true and false, in the semantics of the program. The logical values represent various degrees of truth, which may be combined and propagated by applying the program rules. However, as not any atom can be derived through the program rules, the resulting incomplete information problem is treated here by using assumptions, according to which atoms not derivable may be assigned a (default) logical value. Our approach extends the concept of assumption by employing any value from the considered multi-valued logic as a default value. We define the assumption based multi-valued semantics that extends successful conventional logic programming semantics as the well-founded semantics and the Kripke-Kleene semantics. We show that our semantics has a polynomial data complexity.