Under consideration for publication in Theory and Practice of Logic Programming 1 The Magic of Logical Inference in Probabilistic Programming

Today, many different probabilistic programming languages exist and even more inference mechanisms for these languages. Still, most logic programming based languages use back-ward reasoning based on SLD resolution for inference. While these methods are typically computationally efficient, they often can neither handle infinite and/or continuous distri-butions, nor evidence. To overcome these limitations, we introduce distributional clauses, a variation and extension of Sato’s distribution semantics. We also contribute a novel ap-proximate inference method that integrates forward reasoning with importance sampling, a well-known technique for probabilistic inference. To achieve efficiency, we integrate two logic programming techniques to direct forward sampling. Magic sets are used to focus on relevant parts of the program, while the integration of backward reasoning allows one to identify and avoid regions of the sample space that are inconsistent with the evidence