Quantum coherent spaces and linear logic
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Volume 44 (2010) no. 4, p. 419-441

Quantum Coherent Spaces were introduced by Girard as a quantum framework where to interpret the exponential-free fragment of Linear Logic. Aim of this paper is to extend Girard's interpretation to a subsystem of linear logic with bounded exponentials. We provide deduction rules for the bounded exponentials and, correspondingly, we introduce the novel notion of bounded exponentials of Quantum Coherent Spaces. We show that the latter provide a categorical model of our system. In order to do that, we first study properties of the category of Quantum Coherent Spaces.

DOI : https://doi.org/10.1051/ita/2010021
Classification:  68Q55,  03F52
Keywords: quantum coherent spaces, linear logic, bounded exponentials, denotational semantics, normalization
@article{ITA_2010__44_4_419_0,
     author = {Baratella, Stefano},
     title = {Quantum coherent spaces and linear logic},
     journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications},
     publisher = {EDP-Sciences},
     volume = {44},
     number = {4},
     year = {2010},
     pages = {419-441},
     doi = {10.1051/ita/2010021},
     mrnumber = {2775405},
     language = {en},
     url = {http://www.numdam.org/item/ITA_2010__44_4_419_0}
}
Baratella, Stefano. Quantum coherent spaces and linear logic. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Volume 44 (2010) no. 4, pp. 419-441. doi : 10.1051/ita/2010021. http://www.numdam.org/item/ITA_2010__44_4_419_0/

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