Łukasiewicz Logic with Actions for Neural Networks training
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866909791300878336 |
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| author | Leuştean, Ioana Macovei, Bogdan |
| author_facet | Leuştean, Ioana Macovei, Bogdan |
| contents | Based on the already known connection between multilayer perceptrons and Lukasiewicz logic with rational coefficients, we take a step forward in analyzing its training process using a three-sorted hybrid modal logic: a multilayer perceptron is a logical formula; the actions of the training process are modal operators; the training process is a sequence of logical deductions. Using the proof assistant and the programming language Lean 4, the algorithmic implementation of the training process is certified by logical proofs. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2509_13020 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Łukasiewicz Logic with Actions for Neural Networks training Leuştean, Ioana Macovei, Bogdan Logic in Computer Science Based on the already known connection between multilayer perceptrons and Lukasiewicz logic with rational coefficients, we take a step forward in analyzing its training process using a three-sorted hybrid modal logic: a multilayer perceptron is a logical formula; the actions of the training process are modal operators; the training process is a sequence of logical deductions. Using the proof assistant and the programming language Lean 4, the algorithmic implementation of the training process is certified by logical proofs. |
| title | Łukasiewicz Logic with Actions for Neural Networks training |
| topic | Logic in Computer Science |
| url | https://arxiv.org/abs/2509.13020 |