Cobordisms and commutative categorial grammars

2021/07/19 by Sergey Slavnov, Slavnov, Sergey
Computer Science · #Computation and Language (cs.CL) #FOS: Computer and information sciences #Formal Methods in Verification #Logic in Computer Science (cs.LO) #Logic, Reasoning, and Knowledge #Logic, programming, and type systems

paper · pdf · doi:10.48550/arxiv.2107.08728

openalex publication_date 2021/07/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Physics, Topology, Logic and Computation: A Rosetta Stone
• The Mathematics of Sentence Structure
• Linear logic

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