Fuzzy Datalog∃ over Arbitrary t-Norms

Matthias Lanzinger; Stefano Sferrazza; Przemysław Andrzej Wałęga; Georg Gottlob

doi:10.29007/cngw

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Fuzzy Datalog∃ over Arbitrary t-Norms

19 pages•Published: May 26, 2024

Matthias Lanzinger, Stefano Sferrazza, Przemysław Andrzej Wałęga and Georg Gottlob

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.

Keyphrases: Datalog, Fuzzy Logic, Tuple-generating dependencies

In: Nikolaj Bjorner, Marijn Heule and Andrei Voronkov (editors). Proceedings of 25th Conference on Logic for Programming, Artificial Intelligence and Reasoning, vol 100, pages 426--444

Links:	https://easychair.org/publications/paper/VQVR
	https://doi.org/10.29007/cngw

BibTeX entry

@inproceedings{LPAR2024:Fuzzy_Datalog_over_Arbitrary,
  author    = {Matthias Lanzinger and Stefano Sferrazza and Przemys\{\textbackslash{}l\}aw Andrzej Wa\{\textbackslash{}l\}\textbackslash{}k\{e\}ga and Georg Gottlob},
  title     = {Fuzzy Datalog∃ over Arbitrary t-Norms},
  booktitle = {Proceedings of 25th Conference on Logic for Programming, Artificial Intelligence and Reasoning},
  editor    = {Nikolaj Bj\{\textbackslash{}o\}rner and Marijn Heule and Andrei Voronkov},
  series    = {EPiC Series in Computing},
  volume    = {100},
  pages     = {426--444},
  year      = {2024},
  publisher = {EasyChair},
  bibsource = {EasyChair, https://easychair.org},
  issn      = {2398-7340},
  url       = {https://easychair.org/publications/paper/VQVR},
  doi       = {10.29007/cngw}}

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