Fuzzy Datalog$^\exists$ over Arbitrary t-Norms

• URL: http://arxiv.org/abs/2403.02933v1
• Date: Tue, 5 Mar 2024 12:51:40 GMT
• Title: Fuzzy Datalog$^\exists$ over Arbitrary t-Norms
• Authors: Matthias Lanzinger, Stefano Sferrazza, Przemys{\l}aw A. Wa{\l}\k{e}ga, Georg Gottlob
• Abstract summary: 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. We generalise the standard rule-based language Datalog with existential rules to the 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 associated data with degrees of uncertainty while preserving computational complexity results and the applicability of reasoning techniques established for
• Score: 5.464669506214195
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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