Analyzing Differentiable Fuzzy Implications

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Combining symbolic and neural approaches has gained considerable attention in the AI community, as it is often argued that the strengths and weaknesses of these approaches are complementary. One such trend in the literature are weakly supervised learning techniques that employ operators from fuzzy logics. In particular, they use prior background knowledge described in such logics to help the training of a neural network from unlabeled and noisy data. By interpreting logical symbols using neural networks (or grounding them), this background knowledge can be added to regular loss functions, hence making reasoning a part of learning. In this paper, we investigate how implications from the fuzzy logic literature behave in a differentiable setting. In such a setting, we analyze the differences between the formal properties of these fuzzy implications. It turns out that various fuzzy implications, including some of the most well-known, are highly unsuitable for use in a differentiable learning setting. A further finding shows a strong imbalance between gradients driven by the antecedent and the consequent of the implication. Furthermore, we introduce a new family of fuzzy implications (called sigmoidal implications) to tackle this phenomenon. Finally, we empirically show that it is possible to use Differentiable Fuzzy Logics for semi-supervised learning, and show that sigmoidal implications outperform other choices of fuzzy implications.
Original languageEnglish
Title of host publicationKR2020
Subtitle of host publicationProceedings of the 17th Conference on Principles of Knowledge Representation and Reasoning. Rhodes, Greece. September 12-18, 2020
EditorsDigo Calvanese, Esra Erdem, Michael Thielscher
PublisherIJCAI Organization
Number of pages11
ISBN (Electronic)9780999241172
Publication statusPublished - 18 Sept 2020

Publication series

NameKR Proceedings : Proceedings of the xxth Conference on Principles of Knowledge Representation and Reasoning
PublisherIJCAI Organization
ISSN (Electronic)2334-1033

Bibliographical note

10 pages, 10 figures, accepted to 17th International Conference on Principles of Knowledge Representation and Reasoning (KR 2020). arXiv admin note: substantial text overlap with arXiv:2002.06100.


  • cs.AI
  • cs.LO
  • stat.ML


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