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.

神经符号人工智能领域的主要挑战之一是在神经和符号数据的存在下进行逻辑推理。本文通过将模糊 Datalog 的存在性规则推广到模糊设置，允许使用任意 t - 范数，在保持计算复杂度结果和已建立的推理技术适用性的同时，允许对与不确定度相关的数据进行推理。