Syntactic Requirements for Well-defined Hybrid Probabilistic Logic Programs

The power and expressivity of Probabilistic Logic Programming (PLP) [8, 18] have been utilized to represent many real world situations [2, 9, 14]. Usually, probabilistic logic programs involve only discrete random variables with Bernoulli or Categorical distributions. Numerous solutions emerged to also handle continuous distributions [10, 12, 25], increasing the expressiveness of PLP and giving birth to hybrid probabilistic logic programs, that is, programs that include discrete and continuous random variables. Inference in this type of programs is hard since it combines the complexity of the grounding computation with the intractability of a distribution defined by a mixture of random variables. Usually, inference in general hybrid probabilistic logic programs (i.e., without imposing restrictions on the type of distributions allowed) is done by leveraging knowledge compilation and using external solvers [25] or by sampling [4, 16].