Symbolic knowledge representation and reasoning and deep learning are fundamentally different approaches to artificial intelligence with complementary capabilities. The former are transparent and data-efficient, but they are sensitive to noise and cannot be applied to non-symbolic domains where the data is ambiguous. The latter can learn complex tasks from examples, are robust to noise, but are black boxes; require large amounts of –not necessarily easily obtained– data, and are slow to learn and prone to adversarial examples. Either paradigm excels at certain types of problems where the other paradigm performs poorly. In order to develop stronger AI systems, integrated neuro-symbolic systems that combine artificial neural networks and symbolic reasoning are being sought. In this context, one of the fundamental open problems is how to perform logic-based deductive reasoning over knowledge bases by means of trainable artificial neural networks. This paper provides a brief summary of the authors’ recent efforts to bridge the neural and symbolic divide in the context of deep deductive reasoners. Throughout the paper we will discuss strengths and limitations of models in term of accuracy, scalability, transferability, generalizabiliy, speed, and interpretability, and finally, will talk about possible modifications to enhance desirable capabilities. More specifically, in terms of architectures, we are looking at Memory-augmented networks, Logic Tensor Networks, and compositions of LSTM models to explore their capabilities and limitations in conducting deductive reasoning. We are applying these models on Resource Description Framework (RDF), first-order logic, and the description logic \(\mathcal {E}{\mathscr{L}}^{+}\) respectively.

象征性的知识表示，推理和深度学习是具有互补功能的人工智能的根本不同方法。前者是透明的和数据有效的，但它们对噪声敏感，因此不能应用于数据不明确的非符号域。后者可以从示例中学习复杂的任务，具有较强的抗噪能力，但却是黑匣子。需要大量（不一定很容易获得）数据，并且学习缓慢且容易产生对抗性示例。任一范例都擅长解决其他范例表现不佳的某些类型的问题。为了开发更强大的AI系统，正在寻求将人工神经网络和符号推理相结合的集成神经符号系统。在这种情况下，根本的开放问题之一是如何通过可训练的人工神经网络对知识库执行基于逻辑的演绎推理。本文简要概述了作者在深度演绎推理机的背景下弥合神经和符号鸿沟的最新努力。在整篇文章中，我们将讨论模型在准确性，可伸缩性，可传递性，通用性，速度和可解释性方面的优势和局限性，最后将讨论为增强所需功能而可能进行的修改。更具体地说，在体系结构方面，我们正在研究内存增强网络，逻辑张量网络和LSTM模型的组成，以探索其在演绎推理中的能力和局限性。\（\ mathcal {E} {\ mathscr {L}} ^ {+} \）。