The Russell—Prawitz modality

Mathematical Structures in Computer Science

Volumn 11, Issue 4, 2001, Pages 541-554

  Aczel, Peter ^a  

^a UNIVERSITY OF MANCHESTER   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 4444312149     PISSN: 09601295     EISSN: 14698072     Source Type: Journal    
DOI: 10.1017/S0960129501003309     Document Type: Article

References (22)

1. Aczel, P. (1999) On Relating Type Theories and Set Theories. In: Types '98. Springer-Verlag Lecture Notes in Computer Science 1657.
2. Barras E. (1996) The Coq Proof Assistant Reference Manual, Version 6.1. INRIA Technical Report.
3. Bell, J. (1988) Toposes and Local Set Theories: An Introduction, Oxford Logic Guides 14, Clarendon Press, Oxford.
4. Benton, P.N., Bierman, G.M. and de Paiva, V.C.V. (1998) Computational types from a logical perspective. J. Functional Programming 8 (2) 177–193. Coquand, T. (1990) Metamathematical Investigations of a Calculus of Constructions. In: Oddifredi, P. (ed.) Logic and Computer Science, Academic Press.
5. Fairtlough, M. and Mendler, M. (1997) Propositional Lax Logic. Information and Computation 137 (1) 1–33.
6. Friedman, H. (1978) Classically and intuitionistically provably recursive functions. In: Muller, G.H. and Scott, D.S. (eds.) Higher Set Theory. Springer-Verlag Lecture Notes in Mathematics 669 21–27.
7. Fourman, M.P. and Scott, D.S. (1979) Sheaves and Logic. In: Fourman, M.P., Mulvey, C.J. and Scott, D.S. (eds.) Applications of Sheaves. Springer-Verlag Lecture Notes in Mathematics 753 302–401.
8. Girard, J.Y. (1971) Une extension de l'interpretation de Godel a l'analyse, et son application a l'elimination des coupures dans l'analyse et la theorie des types. In: Fenstad, J. E. (ed.) Proceedings of the Second Scandinavian Logic Symposium, Studies in Logic, North Holland 63–92.
9. Girard, J.Y., Lafont, Y. and Taylor, P. (1990) Proofs and Types, Cambridge Tracts in Theoretical Computer Science 7, Cambridge University Press.
10. Johnstone, P. (1982) Stone Spaces, Cambridge Studies in Advanced Mathematics 3, Cambridge University Press.
11. Leivant, D. (1985) Syntactic translations and provably recursive functions. Journal of Symbolic Logic 50 (3) 682–688.
12. Luo, Z. (1994) Computation and Reasoning: A Type Theory for Computer Science, Clarendon Press, Oxford.
13. Luo, Z. and Pollack, R. (1992) LEGO Proof Development System: User's Manual. Edinburgh University Computer Science Department Technical Report, ECS-LFCS 92-211.
14. Martin-Lof, P. (1984) Intuitionistic type Theory, Studies in Proof Theory, Bibliopolis.
15. Moggi, E. (1989) Computational lambda-calculus and monads. Proceedings of Symposium on Logic in Computer Science 14–23.
16. Moggi, E. (1991) Notions of Computation and monads. Information and Control 93 (1) 55–92.
17. Murthy, C. (1991) An evaluation semantics for classical proofs. In: Proceedings, Sixth Annual IEEE Symposium on Logic in Computer Science Amsterdam 96–107.
18. Prawitz, D. (1965) Natural Deduction: A Proof Theoretical Study. Acta Universitas Stockholmiensis Stockholm Studies in Philosophy 3, Almqvist and Wiksell, Stockholm.
19. Prawitz, D. and Malmnas, P. (1968) A survey of some connections between classical intuitionistic and minimal logic. In: Schmidt, H., Schtte, K. and Thiele, H. (eds.) Contributions to Mathematical Logic, North Holland Studies in Logic 215–229.
20. Russell, B. (1903) The Principles of Mathematics, George, Allen and Unwin Ltd. (2nd edition 1937).
21. Russell, B. (1906) The Theory of Implication. Amer. J. Mathematics 28 159–202.
22. Simmons, H. (1978) A framework for topology. In: Macintyre, A., Pacholski, L. and Paris, J. (eds.) Logic Colloquium 77. Studies in Logic and the Foundations of Mathematics 96, North Holland Publishing Co. 239–251.