Fuzzy Datalog$^\exists$ over Arbitrary t-Norms
This work addresses the problem of integrating neural and symbolic data for AI researchers, but it is incremental as it extends existing Datalog frameworks.
The authors tackled the challenge of performing logical reasoning with heterogeneous data sources in Neuro-Symbolic AI by generalizing Datalog with existential rules to a fuzzy setting using arbitrary t-norms, preserving computational complexity and enabling reasoning with uncertain data.
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.