Probabilistic Answer Set Programming under the credal semantics (PASP) extends Answer Set Programming with probabilistic facts that represent uncertain information. The probabilistic facts are discrete with Bernoulli distributions. However, several real-world scenarios require a combination of both discrete and continuous random variables. In this paper, we extend the PASP framework to support continuous random variables and propose Hybrid Probabilistic Answer Set Programming (HPASP). Moreover, we discuss, implement, and assess the performance of two exact algorithms based on projected answer set enumeration and knowledge compilation and two approximate algorithms based on sampling. Empirical results, also in line with known theoretical results, show that exact inference is feasible only for small instances, but knowledge compilation has a huge positive impact on the performance. Sampling allows handling larger instances, but sometimes requires an increasing amount of memory. Under consideration in Theory and Practice of Logic Programming (TPLP).

翻译：基于信任语义的概率答案集编程（PASP）通过引入表示不确定信息的概率事实，扩展了答案集编程。现有PASP中的概率事实均为服从伯努利分布的离散变量。然而，许多现实场景需要同时处理离散与连续随机变量。本文扩展了PASP框架以支持连续随机变量，提出了混合概率答案集编程（HPASP）。此外，我们讨论、实现并评估了两种基于投影答案集枚举与知识编译的精确算法，以及两种基于采样的近似算法。实验结果表明（与已知理论结论一致）：精确推理仅适用于小规模实例，但知识编译能显著提升性能；采样方法可处理更大规模实例，但有时需要消耗递增的内存资源。本文已投稿至《逻辑编程理论与实践》（TPLP）。