Probabilistic Logic Programming (PLP) under the distribution semantics is a leading approach to practical reasoning under uncertainty. An advantage of the distribution semantics is its suitability for implementation as a Prolog or Python library, available through two well-maintained implementations, namely ProbLog and cplint/PITA. However, current formulations of the distribution semantics use point-probabilities, making it difficult to express epistemic uncertainty, such as arises from, for example, hierarchical classifications from computer vision models. Belief functions generalize probability measures as non-additive capacities and address epistemic uncertainty via interval probabilities. This paper introduces interval-based Capacity Logic Programs based on an extension of the distribution semantics to include belief functions and describes properties of the new framework that make it amenable to practical applications.
