A Semantic Framework for Neuro-Symbolic Computing

• URL: http://arxiv.org/abs/2212.12050v4
• Date: Sat, 20 Jul 2024 19:42:36 GMT
• Title: A Semantic Framework for Neuro-Symbolic Computing
• Authors: Simon Odense, Artur d'Avila Garcez,
• Abstract summary: We provide a formal definition of semantic encoding, specifying the components and conditions under which a knowledge-base can be encoded. We show that many neuro-symbolic approaches are accounted for by this definition. This is expected to provide a guidance to future neuro-symbolic encodings by placing them in the broader context of the semantic encoding of entire families of existing neuro-symbolic systems.
• Score: 0.36832029288386137
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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 throughout the years, and with an 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 of the application of 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 a guidance to future neuro-symbolic encodings by placing them in the broader context of the semantic encoding of entire families of existing neuro-symbolic systems. The paper is hoped 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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