Differentiable Fuzzy $\mathcal{ALC}$: A Neural-Symbolic Representation Language for Symbol Grounding

TL;DR

This paper introduces differentiable fuzzy , a neural-symbolic language that unifies neural models with  knowledge bases for improved symbol grounding, demonstrated by enhanced image object detection in low-resource settings.

Contribution

It proposes a novel differentiable fuzzy  framework that integrates  logic with neural models, enabling semantic consistency and improved unsupervised symbol grounding.

Findings

Improves image object detection performance in low-resource scenarios.

Enforces semantic consistency between neural grounding and  knowledge bases.

Demonstrates effectiveness of rule-based loss in neural-symbolic grounding.

Abstract

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.