The Magic of Logical Inference in Probabilistic Programming

TL;DR

This paper introduces distributional clauses and a novel approximate inference method combining forward reasoning with importance sampling, enhancing probabilistic logic programming's ability to handle complex distributions and evidence.

Contribution

It extends Sato's distribution semantics with distributional clauses and develops an efficient inference technique integrating forward and backward reasoning.

Findings

Effective handling of infinite and continuous distributions.

Improved inference efficiency through combined reasoning techniques.

Ability to incorporate evidence into probabilistic logic inference.

Abstract

Today, many different probabilistic programming languages exist and even more inference mechanisms for these languages. Still, most logic programming based languages use backward reasoning based on SLD resolution for inference. While these methods are typically computationally efficient, they often can neither handle infinite and/or continuous distributions, nor evidence. To overcome these limitations, we introduce distributional clauses, a variation and extension of Sato's distribution semantics. We also contribute a novel approximate 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.