  In probabilistic reasoning, the traditionally discrete domain has been
elevated to the hybrid domain encompassing additionally continuous random
variables. Inference in the hybrid domain, however, usually necessitates to
condone trade-offs on either the inference on discrete or continuous random
variables. We introduce a novel approach based on weighted model integration
and algebraic model counting that circumvents these trade-offs. We then show
how it supports knowledge compilation and exact probabilistic inference.
Moreover, we introduce the hybrid probabilistic logic programming language
HAL-ProbLog, an extension of ProbLog, to which we apply our inference approach.
