One of the main challenges in the area of Neuro-Symbolic AI is to perform logical reasoning in the presence of both neural and symbolic data. This requires combining heterogeneous data sources such as knowledge graphs, neural model predictions, structured databases, crowd-sourced data, and many more. To allow for such reasoning, we generalise the standard rule-based language Datalog with existential rules (commonly referred to as tuple-generating dependencies) to the fuzzy setting, by allowing for arbitrary t-norms in the place of classical conjunctions in rule bodies. The resulting formalism allows us to perform reasoning about data associated with degrees of uncertainty while preserving computational complexity results and the applicability of reasoning techniques established for the standard Datalog setting. In particular, we provide fuzzy extensions of Datalog chases which produce fuzzy universal models and we exploit them to show that in important fragments of the language, reasoning has the same complexity as in the classical setting.

翻译：神经符号人工智能领域的主要挑战之一是在同时包含神经数据和符号数据的环境中进行逻辑推理。这需要整合异构数据源，如知识图谱、神经模型预测、结构化数据库、众包数据等。为实现此类推理，我们将基于标准规则的语言Datalog（含存在规则，通常称为元组生成依赖）泛化到模糊场景，允许在规则体中使用任意t-模替代经典合取。由此形成的框架支持对带有不确定性程度的数据进行推理，同时保持计算复杂度结果以及标准Datalog推理技术的适用性。具体而言，我们提供了Datalog追逐的模糊扩展，可生成模糊通用模型，并利用这些模型证明：在该语言的重要片段中，推理复杂度与经典场景相同。