Neural networks as fuzzy logic formulas
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866910190694039552 |
|---|---|
| author | Heiman, Damian Kuusisto, Antti Turunen, Esko |
| author_facet | Heiman, Damian Kuusisto, Antti Turunen, Esko |
| contents | Neural networks are a fundamental aspect of modern artificial intelligence, playing a key role in various important machine learning architectures including transformers and graph neural networks. Recently, logical characterisations have been used to study the expressive power of many machine learning architectures, but logical characterisations of plain neural networks have received less attention. In this paper, we provide fuzzy logic characterisations of rational-weight ReLU-activated neural networks via two well-established fuzzy logics: Rational Pavelka Logic RPL (and extensions thereof) and (fragments of) $\mathit{L Π} \frac{1}{2}$. The activation values of the neural networks are allowed to be arbitrary real numbers. We also provide fuzzy logic characterisations of a generalised polynomial ring over $\mathbb{Q}$ in countably many variables where the use of the ReLU-function is permitted. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_03064 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Neural networks as fuzzy logic formulas Heiman, Damian Kuusisto, Antti Turunen, Esko Logic in Computer Science F.4.1; F.1.1; I.2.0 Neural networks are a fundamental aspect of modern artificial intelligence, playing a key role in various important machine learning architectures including transformers and graph neural networks. Recently, logical characterisations have been used to study the expressive power of many machine learning architectures, but logical characterisations of plain neural networks have received less attention. In this paper, we provide fuzzy logic characterisations of rational-weight ReLU-activated neural networks via two well-established fuzzy logics: Rational Pavelka Logic RPL (and extensions thereof) and (fragments of) $\mathit{L Π} \frac{1}{2}$. The activation values of the neural networks are allowed to be arbitrary real numbers. We also provide fuzzy logic characterisations of a generalised polynomial ring over $\mathbb{Q}$ in countably many variables where the use of the ReLU-function is permitted. |
| title | Neural networks as fuzzy logic formulas |
| topic | Logic in Computer Science F.4.1; F.1.1; I.2.0 |
| url | https://arxiv.org/abs/2605.03064 |