Incremental Monoidal Grammars
Formal Languages and Automata Theory
2020-01-13 v2 Artificial Intelligence
Logic in Computer Science
Abstract
In this work we define formal grammars in terms of free monoidal categories, along with a functor from the category of formal grammars to the category of automata. Generalising from the Booleans to arbitrary semirings, we extend our construction to weighted formal grammars and weighted automata. This allows us to link the categorical viewpoint on natural language to the standard machine learning notion of probabilistic language model.
Cite
@article{arxiv.2001.02296,
title = {Incremental Monoidal Grammars},
author = {Dan Shiebler and Alexis Toumi and Mehrnoosh Sadrzadeh},
journal= {arXiv preprint arXiv:2001.02296},
year = {2020}
}