Quantum coherent spaces and linear logic
Dipartimento di Matematica, Università di Trento, via
Sommarive 14, 38050 Povo, Italy. email@example.com; firstname.lastname@example.org
Accepted: 14 September 2010
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.
Mathematics Subject Classification: 68Q55 / 03F52
Key words: Quantum coherent spaces / linear logic / bounded exponentials / denotational semantics / normalization
© EDP Sciences, 2010