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.

本文提出了可微模糊 ALC 作为神经符号表示语言并定义层次化损失和基于规则的损失函数用于符号接地问题的 DF-ALC，其实验结果表明 DF-ALC 可以以无监督的方式改善图像目标检测器的性能，即使在低资源情况下。

可微模糊 ALC: 一种神经符号表示语言用于符号基础模型

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

Neural-symbolic computing (NeSy), which pursues the integration of the
symbolic and statistical paradigms of cognition, has been an active research
area of Artificial Intelligence (AI) for many years. As NeSy shows promise of
reconciling the advantages of reasoning and interpretability of symbolic
representation and robust learning in neural networks, it may serve as a
catalyst for the next generation of AI. In the present paper, we provide a
systematic overview of the important and recent developments of research on
NeSy AI. Firstly, we introduce study history of this area, covering early work
and foundations. We further discuss background concepts and identify key
driving factors behind the development of NeSy. Afterward, we categorize recent
landmark approaches along several main characteristics that underline this
research paradigm, including neural-symbolic integration, knowledge
representation, knowledge embedding, and functionality. Then, we briefly
discuss the successful application of modern NeSy approaches in several
domains. Finally, we identify the open problems together with potential future
research directions. This survey is expected to help new researchers enter this
rapidly-developing field and accelerate progress towards data-and
knowledge-driven AI.

本文介绍了神经符号计算（NeSy）领域的重要和最新研究发展，包括研究历史，背景知识，关键驱动因素以及主要特征。文章讨论了该领域的一些重要应用并针对目前存在的问题提出了新的研究方向，以期进一步推动以数据和知识为驱动的 AI 的研究进展。

面向数据和知识驱动的人工智能：神经符号计算综述

Towards Data-and Knowledge-Driven Artificial Intelligence: A Survey on Neuro-Symbolic Computing

Neural-symbolic computing has now become the subject of interest of both
academic and industry research laboratories. Graph Neural Networks (GNN) have
been widely used in relational and symbolic domains, with widespread
application of GNNs in combinatorial optimization, constraint satisfaction,
relational reasoning and other scientific domains. The need for improved
explainability, interpretability and trust of AI systems in general demands
principled methodologies, as suggested by neural-symbolic computing. In this
paper, we review the state-of-the-art on the use of GNNs as a model of
neural-symbolic computing. This includes the application of GNNs in several
domains as well as its relationship to current developments in neural-symbolic
computing.

本文综述了图神经网络作为神经符号计算模型的应用现状和在多个领域中的关系，这反映了对改进人工智能系统的可解释性、解释性和信任度的需求。