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Quantum coherent spaces and linear logic

Published online by Cambridge University Press:  28 October 2010

Stefano Baratella
Stefano Baratella*
Affiliation:
Dipartimento di Matematica, Università di Trento, via Sommarive 14, 38050 Povo, Italy. baratell@science.unitn.it; stefano.baratella@unitn.it
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Abstract

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.

Keywords

Quantum coherent spaceslinear logicbounded exponentialsdenotational semanticsnormalization
Type
Research Article
Information
RAIRO - Theoretical Informatics and Applications , Volume 44 , Issue 4 , October 2010 , pp. 419 - 441
Copyright
© EDP Sciences, 2010

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