This thesis focuses on advancing probabilistic logic programming (PLP), which combines probability theory for uncertainty and logic programming for relations. The thesis aims to extend PLP to support both discrete and continuous random variables, which is necessary for applications with numeric data. The first contribution is the introduction of context-specific likelihood weighting (CS-LW), a new sampling algorithm that exploits context-specific independencies for computational gains. Next, a new hybrid PLP, DC#, is introduced, which integrates the syntax of Distributional Clauses with Bayesian logic programs and represents three types of independencies: i) conditional independencies (CIs) modeled in Bayesian networks; ii) context-specific independencies (CSIs) represented by logical rules, and iii) independencies amongst attributes of related objects in relational models expressed by combining rules. The scalable inference algorithm FO-CS-LW is introduced for DC#. Finally, the thesis addresses the lack of approaches for learning hybrid PLP from relational data with missing values and (probabilistic) background knowledge with the introduction of DiceML, which learns the structure and parameters of hybrid PLP and tackles the relational autocompletion problem. The conclusion discusses future directions and open challenges for hybrid PLP.

翻译：本论文致力于推进概率逻辑程序设计（PLP），该领域将处理不确定性的概率论与处理关系的逻辑程序设计相结合。论文旨在扩展PLP以同时支持离散型和连续型随机变量，这对于处理数值数据的应用至关重要。第一个贡献是引入上下文特定似然加权（CS-LW），这是一种利用上下文特定独立性实现计算增益的新采样算法。其次，引入了一种新的混合PLP——DC#，它统一了分布子句的语法与贝叶斯逻辑程序，并表征了三类独立性：i）贝叶斯网络中建模的条件独立性（CI）；ii）由逻辑规则表示的上下文特定独立性（CSI）；以及iii）通过组合规则表达的关系模型中相关对象属性间的独立性。针对DC#提出了可扩展推理算法FO-CS-LW。最后，针对目前缺乏从含缺失值的关系数据及（概率化）背景知识中学习混合PLP方法的问题，论文引入了DiceML——该算法能够学习混合PLP的结构与参数，并解决关系自动补全问题。结论部分讨论了混合PLP的未来方向与开放性挑战。