Probabilistic and Truth-functional Many-valued Logic Programming Justus-liebig- Universit at Gieeen Ifig Research Report Probabilistic and Truth-functional Many-valued Logic Programming

We introduce probabilistic many-valued logic programs in which the implication connective is interpreted as material implication. We show that probabilistic many-valued logic programming is computationally more complex than classical logic programming. More precisely, some deduction problems that are P-complete for classical logic programs are shown to be co-NP-complete for probabilistic many-valued logic programs. We then focus on many-valued logic programming in Pr ? n as an approximation of probabilistic many-valued logic programming. Surprisingly, many-valued logic programs in Pr ? n have both a probabil-istic semantics in probabilities over a set of possible worlds and a truth-functional semantics in the nite-valued Lukasiewicz logics L n. Moreover, many-valued logic programming in Pr ? n has a model and xpoint characterization, a proof theory, and computational properties that are very similar to those of classical logic programming. We especially introduce the proof theory of many-valued logic programming in Pr ? n and show its soundness and completeness.