A Neuro-Symbolic Approach to Symbol Grounding for ALC Ontologies
Keywords: symbol grounding, ontology embedding, neuro-symbolic computing
Abstract: Neural-symbolic computing aims at integrating robust neural learning and sound symbolic reasoning into a single framework, 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-ALC) for this role, as a neural-symbolic approach with the desired semantics of $\mathcal{ALC}$. DF-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 prove soundness of the semantics of DF-ALC under the open-world assumption and soundness of learning to ground for a DF-ALC ontology. We further define a rule-based loss for DF-ALC adapting to semantic image interpretation. The experiment results show that DF-ALC with rule-based loss can improve the performance of object detectors.
Submission Number: 19
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