论文标题

神经符号计算的语义框架

A Semantic Framework for Neuro-Symbolic Computing

论文作者

Odense, Simon, Garcez, Artur d'Avila

论文摘要

神经符号AI的领域旨在从神经网络和符号系统的组合中受益。该领域的基石是将符号知识翻译或编码为神经网络。尽管已经提出了许多神经符号的方法和方法,并且近年来随着大幅增长,但尚无对编码的共同定义,这些定义可以实现神经符号方法的精确,理论上的比较。本文通过引入神经符号AI的语义框架来解决此问题。我们首先提供对语义编码的正式定义,指定可以通过神经网络正确编码知识库的组件和条件。然后,我们证明了许多神经符号方法是由此定义解释的。我们提供了许多示例和对应证明,将提出的框架应用于各种形式的知识表示形式的神经编码。乍一看,许多人的神经符号方法被证明属于拟议的形式化。预计这将通过将其置于现有神经符号系统的整个家庭语义编码的更广泛背景下,为未来的神经符号编码提供指导。该论文希望有助于介绍提供神经符号AI理论和深度学习语义的理论的讨论。

The field of neuro-symbolic AI aims to benefit from the combination of neural networks and symbolic systems. A cornerstone of the field is the translation or encoding of symbolic knowledge into neural networks. Although many neuro-symbolic methods and approaches have been proposed, and with a large increase in recent years, no common definition of encoding exists that can enable a precise, theoretical comparison of neuro-symbolic methods. This paper addresses this problem by introducing a semantic framework for neuro-symbolic AI. We start by providing a formal definition of semantic encoding, specifying the components and conditions under which a knowledge-base can be encoded correctly by a neural network. We then show that many neuro-symbolic approaches are accounted for by this definition. We provide a number of examples and correspondence proofs applying the proposed framework to the neural encoding of various forms of knowledge representation. Many, at first sight disparate, neuro-symbolic methods, are shown to fall within the proposed formalization. This is expected to provide guidance to future neuro-symbolic encodings by placing them in the broader context of semantic encodings of entire families of existing neuro-symbolic systems. The paper hopes to help initiate a discussion around the provision of a theory for neuro-symbolic AI and a semantics for deep learning.

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