Prolog Extensions to Many{Valued Logics

The aim of this paper is to show that a restriction of a logical language to clauses like Horn clauses, as they are used in Prolog, applied to 0,1]{valued logics leads to calculi with a sound and complete proof theory. In opposition to other models where generally the set of axioms as well as the deduction schemata are enriched we restrict ourselves to a simple modiication of the deduction rules of classical logic without adding new axioms. In our model the truth values from the unit interval can be interpreted in a probabilistic sense, so that a value between 0 and 1 is not just intuitively interpreted as a `degree of truth'.