Differentiable Fuzzy ALC: A Neural-Symbolic Representation Language for Symbol Grounding

Neural-symbolic computing aims at integrating robust neural learning and sound symbolic reasoning into a single framework, so as to leverage the complementary strengths of both of these, seemingly unrelated (maybe even contradictory) AI paradigms. The central challenge in neural-symbolic computing is to unify the formulation of neural learning and symbolic reasoning into a single framework with common semantics, that is, to seek a joint representation between a neural model and a logical theory that can support the basic grounding learned by the neural model and also stick to the semantics of the logical theory. In this paper, we propose differentiable fuzzy ALC (DF-ALC) for this role, as a neural-symbolic representation language with the desired semantics. DF-ALC unifies the description logic ALC and neural models for symbol grounding; in particular, it infuses an ALC knowledge base into neural models through differentiable concept and role embeddings. We define a hierarchical loss to the constraint that the grounding learned by neural models must be semantically consistent with ALC knowledge bases. And we find that capturing the semantics in grounding solely by maximizing satisfiability cannot revise grounding rationally. We further define a rule-based loss for DF adapting to symbol grounding problems. The experiment results show that DF-ALC with rule-based loss can improve the performance of image object detectors in an unsupervised learning way, even in low-resource situations.