Lambek pregroups are Frobenius spiders in preorders
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.
 Publication:

arXiv eprints
 Pub Date:
 May 2021
 arXiv:
 arXiv:2105.03038
 Bibcode:
 2021arXiv210503038P
 Keywords:

 Mathematics  Category Theory;
 Computer Science  Computation and Language;
 Computer Science  Formal Languages and Automata Theory;
 Computer Science  Logic in Computer Science;
 Mathematics  Logic;
 68Q42;
 03B47;
 68T50;
 03B65;
 18A15;
 18B35;
 18D10;
 18B10;
 03B70;
 91F20;
 F.4.2;
 I.2.7;
 I.2.6
 EPrint:
 21 pages, 16 diagrams. Final journal version: DOI kindly inserted by Fosco Loregian