Cobordisms and commutative categorial grammars

TL;DR

This paper introduces a surface-based representation of abstract categorial grammars using cobordisms, connecting graph-based structures with linear logic to enhance linguistic modeling.

Contribution

It presents a novel surface representation of abstract categorial grammars via cobordisms and develops linear logic grammars based on this framework.

Findings

Cobordisms serve as a concrete surface model for categorial grammars.

Linear logic grammars are formulated directly on cobordisms.

The approach generalizes linear logic proof-nets for linguistic applications.

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.