Many-Valued First-Order Logics with Probabilistic Semantics

We present n-valued rst-order logics with a purely proba-bilistic semantics. We then introduce a new probabilistic semantics of n-valued rst-order logics that lies between the purely probabilistic semantics and the truth-functional semantics of the n-valued Lukasiewicz logics Ln. Within this semantics, closed formulas of classical rst-order logics that are logically equivalent in the classical sense also have the same truth value under all n-valued interpretations. Moreover, this semantics is shown to have interesting computational properties. More precisely, n-valued logical consequence in disjunctive logic programs with n-valued disjunctive facts can be reduced to classical logical consequence in n ?1 layers of classical disjunctive logic programs. Moreover, we show that n-valued logic programs have a model and a xpoint semantics that are very similar to those of classical logic programs. Finally, we show that some important deduction problems in n-valued logic programs have the same computational complexity like their classical counterparts.