On quantum logic as multiplicative linear logic with categorical semantics in non-cartesian monoidal categories such as cobordism categories:
Sergey Slavnov, From proof-nets to bordisms: the geometric meaning of multiplicative connectives, Mathematical Structures in Computer Science 15 06 (2005) 1151-1178 [doi:10.1017/S0960129505004974]
Sergey Slavnov, Geometrical semantics for linear logic (multiplicative fragment), Theoretical Computer Science 357 1-3 (2006) 215-229 [doi:10.1016/j.tcs.2006.03.020]
Sergey Slavnov, Coherent phase spaces. Semiclassical semantics, Annals of Pure and Applied Logic
Volume 131, Issues 1–3, January 2005, Pages 177-225, doi:10.1016/j.apal.2004.05.003.
Sergey Slavnov, On Banach spaces of sequences and free linear logic exponential modality, Math. Struct. Comp. Sci. 29 (2019) 215-242 [arXiv:1509.03853]
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