Two approaches to AI, neural networks and symbolic systems, have been proven very successful for an array of AI problems. However, neither has been able to achieve the general reasoning ability required for human-like intelligence. It has been argued that this is due to inherent weaknesses in each approach. Luckily, these weaknesses appear to be complementary, with symbolic systems being adept at the kinds of things neural networks have trouble with and vice-versa. The field of neural-symbolic AI attempts to exploit this asymmetry by combining neural networks and symbolic AI into integrated systems. Often this has been done by encoding symbolic knowledge into neural networks. Unfortunately, although many different methods for this have been proposed, there is no common definition of an encoding to compare them. We seek to rectify this problem by introducing a semantic framework for neural-symbolic AI, which is then shown to be general enough to account for a large family of neural-symbolic systems. We provide a number of examples and proofs of the application of the framework to the neural encoding of various forms of knowledge representation and neural network. These, at first sight disparate approaches, are all shown to fall within the framework's formal definition of what we call semantic encoding for neural-symbolic AI.

翻译：两种人工智能方法——神经网络与符号系统——已被证明在众多人工智能问题上非常成功。然而，这两种方法都未能实现类人智能所需的通用推理能力。研究表明，这源于每种方法固有的缺陷。幸运的是，这些缺陷似乎具有互补性：符号系统擅长处理神经网络难以应对的问题，反之亦然。神经符号人工智能领域试图通过将神经网络与符号人工智能整合为集成系统来利用这种非对称性。常见做法是将符号知识编码到神经网络中。遗憾的是，尽管已提出多种编码方法，但目前缺乏统一的编码定义来进行比较。本文通过引入神经符号人工智能的语义框架来弥补这一缺陷，并证明该框架具有足够通用性，可涵盖大量神经符号系统。我们提供了框架应用于多种知识表示形式与神经网络神经编码的若干实例与证明。这些初看起来迥异的方法，均被证明符合该框架对所谓"神经符号人工智能语义编码"的形式化定义。