Quantum coherent spaces and linear logic

Stefano Baratella

RAIRO - Theoretical Informatics and Applications (2011)

  • 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 44.4 (2011): 419-441. <http://eudml.org/doc/193069>.

@article{Baratella2011,
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},
keywords = {Quantum coherent spaces; linear logic; bounded exponentials; denotational semantics; normalization; quantum coherent spaces},
language = {eng},
month = {2},
number = {4},
pages = {419-441},
publisher = {EDP Sciences},
title = {Quantum coherent spaces and linear logic},
url = {http://eudml.org/doc/193069},
volume = {44},
year = {2011},
}

TY - JOUR
AU - Baratella, Stefano
TI - Quantum coherent spaces and linear logic
JO - RAIRO - Theoretical Informatics and Applications
DA - 2011/2//
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; quantum coherent spaces
UR - http://eudml.org/doc/193069
ER -

References

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  1. S. Abramsky and R. Jagadeesan, Games and full completeness for multiplicative linear logic. J. Symb. Log.2 (1994) 543–574.  Zbl0822.03007
  2. J.M. Ansemil and K. Floret, The symmetric tensor product of a direct sum of locally convex spaces. Stud. Math.129 (1998) 285–295.  Zbl0931.46005
  3. M. Barr, * -autonomous categories and linear logic. Math. Struct. Comp. Sci.1 (1991) 159–178.  Zbl0777.18006
  4. J.R.B. Cockett and R.A.G. Seely, Proof theory for full intuitionistic linear logic, bilinear logic and MIX categories. Theory and Applications of categories3 (1997) 85–131.  Zbl0879.03022
  5. J.-Y. Girard, Le Point Aveugle II, Cours de logique, Vers l'imperfection. Hermann, Paris (2007).  
  6. J.-Y. Girard, Truth, modality and intersubjectivity. Math. Struct. Comp. Sci.17 (2007) 1153–1167.  Zbl1146.03003
  7. J.-Y. Girard, A. Scedrov and P. Scott. Bounded linear logic: a modular approach to polynomial-time computability. Theoret. Comput. Sci.97 (1992) 1–66.  Zbl0788.03005
  8. S. Mac Lane, Categories for the Working Mathematician. 2nd edition Springer, Berlin (1998).  Zbl0906.18001
  9. R.E. Megginson, An Introduction to Banach Space Theory. Springer, Berlin (1998).  Zbl0910.46008
  10. P.-A. Melliès, Categorical semantics of linear logic, available at mellies/.  URIhttp://www.pps.jussieu.fr/
  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. P. Selinger, Towards a semantics for higher-order quantum computation. Proc. QPL (2004) 127–143.  
  13. J. Weidmann, Linear Operators in Hilbert Spaces. Springer, Berlin (1980).  Zbl0434.47001

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