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 $\mathcal{ALC}$ (DF-$\mathcal{ALC}$) for this role, as a neural-symbolic representation language with the desired semantics. DF-$\mathcal{ALC}$ unifies the description logic $\mathcal{ALC}$ and neural models for symbol grounding; in particular, it infuses an $\mathcal{ALC}$ 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 $\mathcal{ALC}$ 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-$\mathcal{ALC}$ with rule-based loss can improve the performance of image object detectors in an unsupervised learning way, even in low-resource situations.

翻译：神经同步计算的目的是将坚固的神经学习和声音符号推理纳入单一框架,以便利用这两种似乎无关(甚至相互矛盾)的AI范式的互补优势。神经同步计算的核心挑战是将神经学习和符号推理的公式统一成一个具有共同语义的单一框架,也就是说,在神经模型和逻辑理论之间寻求一种联合代表,这种理论可以支持神经模型所学的基本基础,并坚持逻辑理论的语义。在本文中,我们提议对这两种似乎无关(也许甚至相互矛盾)的AI范式的互补优势。神经同步计算的核心挑战是将神经学习和符号推理推理的构成一个具有共同语义的单一框架,即:在神经模型和逻辑模型之间寻求一种联合代表,能够支持神经模型所学基础的美元基值 ALC 和智能模型的精度模型,特别是,我们用一个非数学的值 ALC} ALC} 知识基础(DF$)(D- mainallical develrial develride development a drodu demode) listroy development a disal demodeal demode.