Declarative Probabilistic Logic Programming in Discrete-Continuous Domains

TL;DR

This paper introduces a new declarative semantics and language for hybrid probabilistic logic programming that supports both discrete and continuous variables, along with a novel inference algorithm based on knowledge compilation.

Contribution

It presents the measure semantics, the DC-ProbLog language, and the IALW inference engine, generalizing existing PLP frameworks to hybrid domains.

Findings

Introduced measure semantics for hybrid PLP

Developed DC-ProbLog language for hybrid models

Proposed IALW inference algorithm based on knowledge compilation

Abstract

Over the past three decades, the logic programming paradigm has been successfully expanded to support probabilistic modeling, inference and learning. The resulting paradigm of probabilistic logic programming (PLP) and its programming languages owes much of its success to a declarative semantics, the so-called distribution semantics. However, the distribution semantics is limited to discrete random variables only. While PLP has been extended in various ways for supporting hybrid, that is, mixed discrete and continuous random variables, we are still lacking a declarative semantics for hybrid PLP that not only generalizes the distribution semantics and the modeling language but also the standard inference algorithm that is based on knowledge compilation. We contribute the measure semantics together with the hybrid PLP language DC-ProbLog (where DC stands for distributional clauses) and its inference engine infinitesimal algebraic likelihood weighting (IALW). These have the original distribution semantics, standard PLP languages such as ProbLog, and standard inference engines for PLP based on knowledge compilation as special cases. Thus, we generalize the state of the art of PLP towards hybrid PLP in three different aspects: semantics, language and inference. Furthermore, IALW is the first inference algorithm for hybrid probabilistic programming based on knowledge compilation