NeSyCat: A Monad-Based Categorical Semantics of the Neurosymbolic ULLER Framework
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866918470150520832 |
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| author | Schellhorn, Daniel Romero Mossakowski, Till |
| author_facet | Schellhorn, Daniel Romero Mossakowski, Till |
| contents | ULLER (Unified Language for LEarning and Reasoning) offers a unified first-order logic (FOL) syntax, enabling its knowledge bases to be used directly across a wide range of neurosymbolic systems. The original specification endows this syntax with three pairwise independent semantics: classical, fuzzy, and probabilistic, each accompanied by dedicated semantic rules. We show that these seemingly disparate semantics are all instances of one categorical framework based on monads, the very construct that models side effects in functional programming. This enables the modular addition of new semantics and systematic translations between them. As example, we outline the addition of generalised quantification in Logic Tensor Networks (LTN) to arbitrary (also infinite) domains by extending the Giry monad to probability spaces. In particular, our approach allows a modular implementation of ULLER in Python and Haskell, of which we have published initial versions on GitHub. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_24612 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | NeSyCat: A Monad-Based Categorical Semantics of the Neurosymbolic ULLER Framework Schellhorn, Daniel Romero Mossakowski, Till Artificial Intelligence Logic in Computer Science Category Theory Logic 03B70, 03B52, 18C50, 68T27 F.4.1; I.2.4; I.2.6 ULLER (Unified Language for LEarning and Reasoning) offers a unified first-order logic (FOL) syntax, enabling its knowledge bases to be used directly across a wide range of neurosymbolic systems. The original specification endows this syntax with three pairwise independent semantics: classical, fuzzy, and probabilistic, each accompanied by dedicated semantic rules. We show that these seemingly disparate semantics are all instances of one categorical framework based on monads, the very construct that models side effects in functional programming. This enables the modular addition of new semantics and systematic translations between them. As example, we outline the addition of generalised quantification in Logic Tensor Networks (LTN) to arbitrary (also infinite) domains by extending the Giry monad to probability spaces. In particular, our approach allows a modular implementation of ULLER in Python and Haskell, of which we have published initial versions on GitHub. |
| title | NeSyCat: A Monad-Based Categorical Semantics of the Neurosymbolic ULLER Framework |
| topic | Artificial Intelligence Logic in Computer Science Category Theory Logic 03B70, 03B52, 18C50, 68T27 F.4.1; I.2.4; I.2.6 |
| url | https://arxiv.org/abs/2604.24612 |