Cobordisms and commutative categorial grammars
This work addresses a theoretical problem in formal linguistics and logic for researchers in categorial grammars and linear logic, but it appears incremental as it builds on existing concepts like proof-nets.
The paper tackles the problem of representing abstract categorial grammars by proposing a concrete surface representation using word cobordisms, which are bipartite graphs decorated with words, and introduces linear logic grammars based on cobordisms with classical multiplicative linear logic as a typing system.
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.