Abstract not found

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 probabilistic semantics in probabilities over a set of possible worlds and a truth-functional semantics in the finite-valued Łukasiewicz logics Łn . Moreover, many-valued 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...

The purpose of this paper is to show how the theory of probabilistic argumentation systems can be extended from propositional logic to the more general framework of set constraint logic. The strength of set constraint logic is that logical relations between non-binary variables can be expressed more directly. This simplifies the classical way of modeling knowledge through propositional logic. Building argumentation systems on set constraint logic is therefore useful for improving its capabilities of expressing different forms of uncertain knowledge. 1

Drawing inferences from a set of general constraint clauses is known as a difficult problem. A general approach is based on the idea of eliminating some or all variables involved. In the particular case of propositional logic, this approach leads to a simple procedure that incorporates the well-known resolution principle. The purpose of this paper is to show how the resolution principle can be extended to constraint logic where the knowledge is given as a set of constraint clauses. The result is a general variable elimination method. The paper shows that the elimination problem can always be reduced to the problem of eliminating the variable from a (conjunctive) set of atomic constraints. Variabele elimination has a number of possible applications such as satisfiability testing, hypotheses testing, constraint solving, argumentative reasoning, and many others. 1