# Cobordisms and commutative categorial grammars

@article{Slavnov2021CobordismsAC, title={Cobordisms and commutative categorial grammars}, author={Sergey Slavnov}, journal={ArXiv}, year={2021}, volume={abs/2107.08728} }

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.

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On embedding Lambek calculus into commutative categorial grammars

- Computer Science, Mathematics
- ArXiv
- 2020

The problem of encoding noncommutative operations in ACG turns out possible after enriching the system with new unary operators, and the resulting system allows representing both ACG and Lambek grammars as conservative fragments, while the formalism remains, as it seems to us, rather simple and intuitive. Expand

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