Fuzzy Datalog^∃ over Arbitrary t-Norms
arxiv(2024)
摘要
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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