The Dialectica interpretation of first-order classical affine logic

Theory and Applications of Categories

Volumn 17, Issue , 2006, Pages 49-79

  Shirahata, Masaru ^a  

^a KEIO UNIVERSITY   (Japan)

Author keywords

Categorical logic; Dialectica interpretation; Linear logic

Indexed keywords

EID: 33846486940     PISSN: 1201561X     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (18)

1. Abramsky, S. and Jagadeesan, R. (1994). Games and full completeness for multiplicative linear logic. Journal of Symbolic Logic, 59(2):543 - 574.
2. Abramsky, S., Malacaria, P., and Jagadeesan, R. (2000). Full abstraction for PCF. Information and Computation, 163:409-470.
3. Avigad, J. and Feferman, S. (1998). Gödel's functional ("dialectica") interpretation. In Buss, S., editor, Handbook of Proof Theory, chapter V. Elsevier.
4. Berger, U. (2005). Uniform Heyting arithmetic. Annals of Pure and Applied Logic, 133(1-3):125-148.
5. Cook, S. A. and Urquhart, A. (1993). Functional interpretations of feasibly constructive arithmetic. Annals of Pure and Applied Logic, 63:103-200.
6. de Paiva, V. (1991). The dialectica categories. Technical Report 213, University of Cambridge, Computer Laboratory.
7. de Paiva, V. (2006). Dialectica and chu constructions: Cousins ? In this Volume.
8. Devarajan, H., Hughes, D. J. D., Plotkin, G. D., and Pratt, V. R. (1999). Full completeness of the multiplicative linear logic of chu spaces. In Logic in Computer Science, pages 234-242.
9. Diller, V. J. and Nahm, W. (1974). Eine Variante zur Dialectica- Interpretation der Heyting-Arithmetik endlicher Typen. Archiv für Mathematische Logik und Grundlagenforschung, 16:49-66.
10. Girard, J.-Y. (1987). Linear logic. Theoretical Computer Science, 50:2-102.
11. Girard, J.-Y. (1998). Light linear logic. Information and Computation, 143:175-204.
12. Gödel, K. (1990). Über eine bisher noch nicht benützte Erweiterung des finiten Standpunktes. In Feferman, S., Dawson, Jr., J. W., Kleene, S. C., Moore, G. H., Solovay, R. M., and van Haijenoort, J., editors, Collected Works, volume II, pages 240-251. Oxford University Press.
13. Hindley, J. R. and Seidin, J. P. (1986). Introduction to the Combinators and λ-Calculus. Cambridge University Press.
14. Hintikka, J. (1996). The Principles of Mathematics Revisited. Cambridge University Press.
15. Hyland, J. M. E. (2002). Proof theory in the abstract. Annals of Pure and Applied Logic, 114:43-78.
16. Shoenfield, J. R. (1967). Mathematical Logic. Addison-Wesley.
17. Streicher, T. (2000). A semantic version of the diller-nahm variant of gödel's dialectica interpretation. Available at his web site.
18. Troelstra, A. E., editor, (2000). Metamathematical Investigation of Intuitionistic Arithmetic and Analysis Lecture Notes in Mathematics 344. Springer.