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 hybrid distribution semantics together with the hybrid PLP language DC-ProbLog 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.

翻译：过去三十年间，逻辑编程范式已成功拓展至概率建模、推理与学习领域。由此产生的概率逻辑编程范式及其编程语言，其成功很大程度上归功于声明式语义（即所谓的分布语义）。然而，分布语义仅局限于离散随机变量。尽管概率逻辑编程已通过多种方式扩展以支持混合（即离散与连续随机变量混合）场景，但我们仍缺乏一种既能泛化分布语义与建模语言，又能泛化基于知识编译的标准推理算法的混合概率逻辑编程声明式语义。本文提出混合分布语义、混合概率逻辑编程语言DC-ProbLog及其推理引擎无穷小代数似然加权（IALW）。这些成果将原始分布语义、ProbLog等标准概率逻辑编程语言以及基于知识编译的标准概率逻辑编程推理引擎作为特例纳入框架。由此，我们从语义、语言和推理三个维度将概率逻辑编程的最新技术泛化至混合概率逻辑编程领域。此外，IALW是首个基于知识编译的混合概率编程推理算法。