Lambek pregroups are Frobenius spiders in preorders
arXiv:2105.03038 · doi:10.32408/compositionality-4-1
Abstract
"Spider" is a nickname of special Frobenius algebras, a fundamental structure from mathematics, physics, and computer science. Pregroups are a fundamental structure from linguistics. Pregroups and spiders have been used together in natural language processing: one for syntax, the other for semantics. It turns out that pregroups themselves can be characterized as pointed spiders in the category of preordered relations, where they naturally arise from grammars. The other way around, preordered spider algebras in general can be characterized as unions of pregroups. This extends the characterization of relational spider algebras as disjoint unions of groups. The compositional framework that emerged with the results suggests new ways to understand and apply the basis structures in machine learning and data analysis.
21 pages, 16 diagrams. Final journal version: DOI kindly inserted by Fosco Loregian
References in corpus (10)
- Language Models are Few-Shot Learners
- QNLP in Practice: Running Compositional Models of Meaning on a Quantum Computer
- Mathematical Foundations for a Compositional Distributional Model of Meaning
- The Frobenius anatomy of word meanings I: subject and object relative pronouns
- Quantum Natural Language Processing on Near-Term Quantum Computers
- The Frobenius anatomy of word meanings II: possessive relative pronouns
- Tight spans, Isbell completions and semi-tropical modules
- Functorial Semantics for Partial Theories
- A Frobenius Algebraic Analysis for Parasitic Gaps
- Compositionality for Recursive Neural Networks