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：在过去三十年中,逻辑编程范式成功地扩展了,以支持概率模型、推断和学习;由此形成的概率逻辑编程及其编程语言的范例在很大程度上归功于一种宣示性语义,即所谓的发行语义;然而,发行语义仅限于离散随机变量;虽然在支持混合(即混合离散和连续随机变量)方面,PLP以各种方式扩展了各种支持混合(即混合离散和连续随机变量),但我们仍然缺乏混合PLP的宣示性语义,不仅概括了分发语义和模型语言,而且还基于知识汇编的标准推算算法。因此,我们把混合分发语义与混合的PLPL-ProbLog语言及其推论引擎(IALW)一起贡献了混合语义语义,这是基于知识汇编的特殊案例的原始分发语义、标准PLPPR语言和标准推论引擎。因此,我们把PLPPM语言的状态和代序中三种混合方言文的拼图集化了。