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-v...

We present a domain-theoretic framework for measure theory and integration of bounded real-valued functions with respect to bounded Borel measures on compact metric spaces. The set of normalised Borel measures of the metric space can be embedded into the maximal elements of the normalised probabilistic power domain of its upper space. Any bounded Borel measure on the compact metric space can th...

In “standard” probability theory, one lists all events that are logically possible, and then places a normalized measure over them. This scheme is rather dry. It may happen that the list of possible events is encoded through logical sentences, and one must employ logical reasoning to determine which events are included in probabilistic assessments. It may also happen that probabilistic assessme...