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ARXIV:2604.24612 · NEUROSYMBOLIC AI · SUBMITTED 28 APR · 15:19 UTC · FRESHNESS STALE
ARXIV:2604.24612NEUROSYMBOLIC AISUBMITTED 28 APR · 15:19 UTCFRESHNESS STALEDaniel Romero Schellhorn · Till Mossakowski · arXiv
A categorical framework for unifying neurosymbolic learning and reasoning semantics, enabling modular extensions.
Opportunity summary
Pain A categorical framework for unifying neurosymbolic learning and reasoning semantics, enabling modular extensions.
Evidence 0 refs | 3 sources | 50% coverage
Blocker Evidence unverified
A categorical framework for unifying neurosymbolic learning and reasoning semantics, enabling modular extensions. The original specification endows this syntax with three pairwise independent semantics: classical, fuzzy, and probabilistic, each accompanied by dedicated semantic rules.
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…
ScienceToStartup currently rates this 4.0/10 on the public viability pass. We show that these seemingly disparate semantics are all instances of one categorical framework based on monads, the very construct that models side effects…
Neurosymbolic AI moved forward this cycle; last verified April 2026. Public score 4.0/10. Production flags indicate code availability.
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A categorical framework for unifying neurosymbolic learning and reasoning semantics, enabling modular extensions.
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10.48550/arXiv.2604.24612A categorical framework for unifying neurosymbolic learning and reasoning semantics, enabling modular extensions.
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.
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PROBLEM
A categorical framework for unifying neurosymbolic learning and reasoning semantics, enabling modular extensions. The original specification endows this syntax with three pairwise independent semantics: classical, fuzzy, and probabilistic, each accompanied by dedicated semantic...
METHOD
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 seman...
RESULT
ScienceToStartup currently rates this 4.0/10 on the public viability pass. 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. Code availability is...
WHY NOW
Neurosymbolic AI moved forward this cycle; last verified April 2026. Public score 4.0/10. Production flags indicate code availability.
{"file name": "input.pdf", "number of pages": 42, "author": "Daniel Romero Schellhorn; Till Mossakowski", "title": "NeSyCat: A Monad-Based Categorical Semantics of the Neurosymbolic ULLER Framework"
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A categorical framework for unifying neurosymbolic learning and reasoning semantics, enabling modular extensions.
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