Modified realizability interpretation of classical linear logic

Proceedings - Symposium on Logic in Computer Science

Volumn , Issue , 2007, Pages 431-440

  Oliva, Paulo ^a  

^a QUEEN MARY UNIVERSITY OF LONDON   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

BRANCHING QUANTIFIERS; CATEGORICAL MODEL; CLASSICAL LINEAR LOGIC; LINEAR LOGIC; REALIZABILITY;

COMPUTATION THEORY;

EID: 82755183340     PISSN: 10436871     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/LICS.2007.32     Document Type: Conference Paper

References (21)

1. S. Abramsky and R. Jagadeesan. Games and full completeness for multiplicative linear logic. The Journal of Symbolic Logic, 59(2):543-574, 1994.
2. M. Barr. The Chu construction. Theory and Applications of Categories, 2(2):17-35, 1996.
3. M. Bezem. Strongly majorizable functionals of finite type: a model for bar recursion containing discontinuous functionals. The Journal of Symbolic Logic, 50:652-660, 1985.
4. A. Blass. Questions and answers - a category arising in linear logic, complexity theory, and set theory. In J.-Y. Girard, Y. Lafont, and L. Regnier, editors, Advances in Linear Logic, volume 222, pages 61-81. London Math. Soc. Lecture Notes, 1995.
5. A. Blass and Y. Gurevich. Henkin quantifiers and complete problems. Annals of Pure and Applied Logic, 32:1-16, 1986.
6. J. Diller and W. Nahm. Eine Variant zur Dialecticainterpretation der Heyting Arithmetik endlicher Typen. Arch. Math. Logik Grundlagenforsch, 16:49-66, 1974.
7. F. Ferreira and P. Oliva. Bounded functional interpretation. Annals of Pure and Applied Logic, 135:73-112, 2005. (Pubitemid 41001597)
8. F. Ferreira and P. Oliva. Bounded functional interpretation in feasible analysis. Annals of Pure and Applied Logic, 145:115-129, 2007. (Pubitemid 44858108)
9. J.-Y. Girard. Linear logic. Theoretical Computer Science, 50(1):1-102, 1987.
10. J.-Y. Girard. Towards a geomery of interaction. Contemporary Mathematics, 92, 1989.
11. K. Gödel. Über eine bisher noch nicht benützte Erweiterung des finiten Standpunktes. Dialectica, 12:280-287, 1958.
12. L. Henkin. Some remarks on infinitely long formulas. In Infinitistic methods, pages 167-183. Pergamon Press, New York, and Polish Scientific Publishers, Warsaw, 1961.
13. J. M. E. Hyland. Proof theory in the abstract. Annals of Pure and Applied Logic, 114:43-78, 2002.
14. G. Kreisel. Interpretation of analysis by means of constructive functionals of finite types. In A. Heyting, editor, Constructivity in Mathematics, pages 101-128. North Holland, Amsterdam, 1959.
15. P. Oliva. Unifying functional interpretations. Notre Dame Journal of Formal Logic, 47(2):263-290, 2006.
16. V. C. V. de Paiva. The Dialectica categories. In J. W. Gray and A. Scedrov, editors, Proc. of Categories in Computer Science and Logic, Boulder, CO, 1987, pages 47-62. Contemporary Mathematics, vol 92, American Mathematical Society, 1989.
17. V. C. V. de Paiva. A Dialectica-like model of linear logic. In D. Pitt, D. Rydeheard, P. Dybjer, A. Pitts, and A. Poigné, editors, Category Theory and Computer Science, Manchester, UK, pages 341-356. SpringerVerlag LNCS 389, 1989.
18. V. C. V. de Paiva. Dialectica and Chu constructions: Cousins? Accepted for publication. To appear. Available from http://www.cs.bham.ac.uk/~vdp, 2007.
19. M. Shirahata. The Dialectica interpretation of firstorder classical linear logic. Theory and Applications of Categories, 17(4):49-79, 2006.
20. A. S. Troelstra. Metamathematical Investigation of Intuitionistic Arithmetic and Analysis, volume 344 of Lecture Notes in Mathematics. Springer, Berlin, 1973.
21. A. S. Troelstra. Realizability. In S. R. Buss, editor, Handbook of proof theory, volume 137, pages 408-473. North Holland, Amsterdam, 1998.