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 #cs.CL #cs.LO
paper · pdf · doi:10.48550/arxiv.2107.08728
This is the final version of the previously posted series of drafts on cobordimns and categorial grammars. Concise and, hopefully, much improved presentation, but no new mathematical content compared to preceding versions. arXiv admin note: text overlap with arXiv:1911.03962
arxiv created 2021/07/19 · openalex publication_date 2021/07/19 · arxiv updated 2021/07/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.