Monad-Based Categorical Semantics Unify Neurosymbolic ULLER Framework
ULLER (Unified Language for LEarning and Reasoning) provides a first-order logic syntax for neurosymbolic systems, originally with three independent semantics: classical, fuzzy, and probabilistic. Researchers show these are all instances of a monad-based categorical framework, enabling modular addition of new semantics and systematic translations. They outline adding generalized quantification in Logic Tensor Networks (LTN) to infinite domains via the Giry monad. A modular implementation in Python and Haskell has been published.
Key facts
- ULLER offers a unified first-order logic syntax for neurosymbolic systems.
- Original specification has three pairwise independent semantics: classical, fuzzy, probabilistic.
- These semantics are instances of a monad-based categorical framework.
- Monads model side effects in functional programming.
- New semantics can be added modularly.
- Systematic translations between semantics are enabled.
- Addition of generalized quantification in LTN to infinite domains is outlined.
- Modular implementation in Python and Haskell has been published.
Entities
Institutions
- arXiv