Cobordisms and commutative categorial grammars

• URL: http://arxiv.org/abs/2107.08728v1
• Date: Mon, 19 Jul 2021 09:55:21 GMT
• Title: Cobordisms and commutative categorial grammars
• Authors: Sergey Slavnov
• Abstract summary: We propose a concrete surface representation of abstract categorial grammars in the category of word cobordisms or cowordisms for short. We also introduce and study linear logic grammars, directly based on cobordisms and using classical multiplicative linear logic as a typing system.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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