Cobordisms and commutative categorial grammars
Logic in Computer Science
2021-07-21 v1 Computation and Language
Abstract
We propose a concrete surface representation of abstract categorial grammars in the category of word cobordisms or cowordisms for short, which are certain bipartite graphs decorated with words in a given alphabet, generalizing linear logic proof-nets. We also introduce and study linear logic grammars, directly based on cobordisms and using classical multiplicative linear logic as a typing system.
Cite
@article{arxiv.2107.08728,
title = {Cobordisms and commutative categorial grammars},
author = {Sergey Slavnov},
journal= {arXiv preprint arXiv:2107.08728},
year = {2021}
}
Comments
This is the final version of the previously posted series of drafts on cobordimns and categorial grammars. Concise and, hopefully, much improved presentation, but no new mathematical content compared to preceding versions. arXiv admin note: text overlap with arXiv:1911.03962