Many-Valued First-Order Logics with Probabilistic Semantics

Abstract We present n -valued first-order logics with a purely probabilistic semantics. We then introduce a new probabilistic semantics of n -valued first-order logics that lies between the purely probabilistic semantics and the truth-functional semantics of the n -valued Łukasiewicz logics Ł n. Within this semantics, closed formulas of classical first-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 fixpoint 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.

Authors

• Thomas Lukasiewicz

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