Quantum coherent spaces and linear logic

Stefano Baratella

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications (2010)

  • Volume: 44, Issue: 4, page 419-441
  • ISSN: 0988-3754

Abstract

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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.

How to cite

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Baratella, Stefano. "Quantum coherent spaces and linear logic." RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications 44.4 (2010): 419-441. <http://eudml.org/doc/245629>.

@article{Baratella2010,
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.},
author = {Baratella, Stefano},
journal = {RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications},
keywords = {quantum coherent spaces; linear logic; bounded exponentials; denotational semantics; normalization},
language = {eng},
number = {4},
pages = {419-441},
publisher = {EDP-Sciences},
title = {Quantum coherent spaces and linear logic},
url = {http://eudml.org/doc/245629},
volume = {44},
year = {2010},
}

TY - JOUR
AU - Baratella, Stefano
TI - Quantum coherent spaces and linear logic
JO - RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications
PY - 2010
PB - EDP-Sciences
VL - 44
IS - 4
SP - 419
EP - 441
AB - 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.
LA - eng
KW - quantum coherent spaces; linear logic; bounded exponentials; denotational semantics; normalization
UR - http://eudml.org/doc/245629
ER -

References

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  8. [8] S. Mac Lane, Categories for the Working Mathematician. 2nd edition Springer, Berlin (1998). Zbl0232.18001
  9. [9] R.E. Megginson, An Introduction to Banach Space Theory. Springer, Berlin (1998). Zbl0910.46008
  10. [10] P.-A. Melliès, Categorical semantics of linear logic, available at http://www.pps.jussieu.fr/ mellies/. Zbl1206.03052
  11. [11] B.F. Redmond, Multiplexor categories and models of Soft Linear Logic. Logical foundations of computer science, Lecture Notes in Comput. Sci. 4514, Springer, Berlin (2007) 472–485. Zbl1132.03352
  12. [12] P. Selinger, Towards a semantics for higher-order quantum computation. Proc. QPL (2004) 127–143. 
  13. [13] J. Weidmann, Linear Operators in Hilbert Spaces. Springer, Berlin (1980). Zbl0434.47001

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