NeSyCat: A Monad-Based Categorical Semantics of the Neurosymbolic ULLER Framework

Computer Science > Artificial Intelligence arXiv:2604.24612 (cs) [Submitted on 27 Apr 2026] Title:NeSyCat: A Monad-Based Categorical Semantics of the Neurosymbolic ULLER Framework Authors:Daniel Romero Schellhorn, Till Mossakowski View a PDF of the paper titled NeSyCat: A Monad-Based Categorical Semantics of the Neurosymbolic ULLER Framework, by Daniel Romero Schellhorn and 1 other authors View PDF HTML (experimental) Abstract: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. Comments: 42 pages. Submitted to Neurosymbolic Artificial Intelligence (IOS Press), after extending from a conference paper of NeSy25 Subjects: Artificial Intelligence (cs.AI); Logic in Computer Science (cs.LO); Category Theory (math.CT); Logic (math.LO) MSC classes: 03B70, 03B52, 18C50, 68T27 ACM classes: F.4.1; I.2.4; I.2.6 Cite as: arXiv:2604.24612 [cs.AI] (or arXiv:2604.24612v1 [cs.AI] for this version) https://doi.org/10.48550/arXiv.2604.24612 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Daniel Romero Schellhorn [view email] [v1] Mon, 27 Apr 2026 15:40:15 UTC (63 KB) Full-text links: Access Paper: View a PDF of the paper titled NeSyCat: A Monad-Based Categorical Semantics of the Neurosymbolic ULLER Framework, by Daniel Romero Schellhorn and 1 other authorsView PDFHTML (experimental)TeX Source view license Current browse context: cs.AI < prev | next > new | recent | 2026-04 Change to browse by: cs cs.LO math math.CT math.LO References & Citations NASA ADSGoogle Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv (What is alphaXiv?) Links to Code Toggle CatalyzeX Code Finder for Papers (What is CatalyzeX?) DagsHub Toggle DagsHub (What is DagsHub?) GotitPub Toggle Gotit.pub (What is GotitPub?) Huggingface Toggle Hugging Face (What is Huggingface?) ScienceCast Toggle ScienceCast (What is ScienceCast?) Demos Demos Replicate Toggle Replicate (What is Replicate?) Spaces Toggle Hugging Face Spaces (What is Spaces?) Spaces Toggle TXYZ.AI (What is TXYZ.AI?) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower…

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