Probalistic and truth-functional many-valued logic programming
We introduce probabilistic manyvalued 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 Pcomplete for classical logic programs are ... shown to be coNPcomplete for probabilistic manyvalued logic programs. We then focus on manyvalued logic programming in Pr*n as an approximation of probabilistic manyvalued logic programming. Surprisingly, manyvalued logic programs in Pr*n have both a probabilistic semantics in probabilities over a set of possible worlds and a truthfunctional semantics in the finitevalued Lukasiewicz logics Ln. Moreover, manyvalued logic programming in Pr*n has a model and fixpoint characterization, a proof theory, and computational properties that are very similar to those of classical logic programming. We especially introduce the proof theory of manyvalued logic programming in Pr*n and show its soundness and completeness.
(Anm.: Die Zeichendarstellung in diesem Abstract entspricht nicht der Vorlage)