Analyzing Differentiable Fuzzy Logic Operators

The AI community is increasingly putting its attention towards combining symbolic and neural approaches, as it often argued that the strengths weaknesses of these approaches are complementary. One recent trend in literature weakly supervised learning techniques employ operators from fuzzy logics. In particular, use prior background knowledge described such logics to help training a network unlabeled noisy data. By interpreting logical symbols using networks, this can be added regular loss functions, hence making reasoning part learning. We study, both formally empirically, how large collection logic behave differentiable setting. find many operators, including some most well-known, highly unsuitable A further finding concerns treatment implication logics, shows strong imbalance between gradients driven by antecedent consequent implication. Furthermore, we introduce new family implications (called sigmoidal implications) tackle phenomenon. Finally, empirically show possible Differentiable Fuzzy Logics for semi-supervised learning, compare different practice. that, achieve largest performance improvement over baseline, have resort non-standard combinations which perform well but no longer satisfy usual laws.