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...

In this paper, we propose formulations and algorithms for robust portfolio optimization under both aleatory uncertainty (i.e., natural variability) and epistemic uncertainty (i.e., imprecise probabilistic information) arising from interval data. Epistemic uncertainty is represented using two approaches: (1) moment bounding approach and (2) likelihood-based approach. This paper first proposes a ...

We introduce a new approach to probabilistic logic programming in which probabilities are defined over a set of possible worlds. More precisely, classical program clauses are extended by a subinterval of [0; 1℄ that describes a range for the conditional probability of the head of a clause given its body. We then analyze the complexity of selected probabilistic logic programming tasks. It turns ...

Uncertain information is being taken into account in an increasing number of application fields. In the meantime, abduction has been proved a powerful tool for handling hypothetical reasoning and incomplete knowledge. Probabilistic logical models are suitable framework to handle uncertain information, last decade many probabilistic languages have proposed, as well inference learning systems the...