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| Main Authors: | , |
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| Format: | Preprint |
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2022
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| Online Access: | https://arxiv.org/abs/2212.12050 |
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| _version_ | 1866910717211312128 |
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| author | Odense, Simon Garcez, Artur d'Avila |
| author_facet | Odense, Simon Garcez, Artur d'Avila |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2212_12050 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | A Semantic Framework for Neuro-Symbolic Computing Odense, Simon Garcez, Artur d'Avila Artificial Intelligence 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. |
| title | A Semantic Framework for Neuro-Symbolic Computing |
| topic | Artificial Intelligence |
| url | https://arxiv.org/abs/2212.12050 |