We present dPASP, a novel declarative probabilistic logic programming framework for differentiable neuro-symbolic reasoning. The framework allows for the specification of discrete probabilistic models with neural predicates, logic constraints and interval-valued probabilistic choices, thus supporting models that combine low-level perception (images, texts, etc), common-sense reasoning, and (vague) statistical knowledge. To support all such features, we discuss the several semantics for probabilistic logic programs that can express nondeterministic, contradictory, incomplete and/or statistical knowledge. We also discuss how gradient-based learning can be performed with neural predicates and probabilistic choices under selected semantics. We then describe an implemented package that supports inference and learning in the language, along with several example programs. The package requires minimal user knowledge of deep learning system's inner workings, while allowing end-to-end training of rather sophisticated models and loss functions.

翻译：我们提出dPASP，一种用于可微分神经符号推理的新型声明式概率逻辑编程框架。该框架支持通过神经谓词、逻辑约束和区间值概率选择来指定离散概率模型，从而能够整合低级感知（图像、文本等）、常识推理与（模糊）统计知识。为支持所有这些特性，我们讨论了可用于表达非确定性、矛盾性、不完整性和/或统计知识的概率逻辑程序的若干语义。我们还探讨了如何在选定语义下通过神经谓词和概率选择执行基于梯度的学习。随后，我们描述了一个已实现的支持该语言推理与学习的软件包，并附以若干示例程序。该软件包仅需用户具备极少的深度学习系统内部原理知识，即可实现复杂模型与损失函数的端到端训练。