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.

中文翻译：

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离散连续域中的声明式概率逻辑编程


在过去的三十年里，逻辑编程范式已经成功地扩展到支持概率建模、推理和学习。由此产生的概率逻辑编程 （PLP） 范式及其编程语言的成功在很大程度上归功于声明性语义，即所谓的分布语义。但是，分布语义仅限于离散随机变量。虽然 PLP 已经以各种方式扩展以支持混合，即混合离散和连续随机变量，但我们仍然缺乏混合 PLP 的声明性语义，它不仅概括了分布语义和建模语言，还推广了基于知识编译的标准推理算法。我们将测度语义与混合 PLP 语言 DC-ProbLog（其中 DC 代表分布子句）及其推理引擎无穷小代数似然加权 （IALW） 一起贡献。这些具有原始的分发语义、标准 PLP 语言（如 ProbLog）和基于知识编译的 PLP 标准推理引擎作为特殊情况。因此，我们将 PLP 的技术水平概括为三个不同方面的混合 PLP：语义、语言和推理。此外，IALW 是第一个基于知识编译的混合概率规划推理算法。