On an intuitionistic modal logic

Studia Logica

Volumn 65, Issue 3, 2000, Pages 383-416

  Blerman, G M ^a   De Paiva, V C V ^b  

^a UNIVERSITY OF CAMBRIDGE   (United Kingdom)

^b UNIVERSITY OF BIRMINGHAM   (United Kingdom)

Author keywords

Categorical models; Intuitionistic logic; Modal logic; Proof theory

Indexed keywords

EID: 0042709133     PISSN: 00393215     EISSN: 15728730     Source Type: Journal    
DOI: 10.1023/a:1005291931660     Document Type: Article

References (38)

1. BARBER, A., Linear Type Theories, Semantics and Action Calculi,. PhD thesis, University of Edinburgh, 1997.
2. BENEVIDES, M., and T. MAIBAUM, 'A constructive presentation for the modal connective of necessity', Journal of Logic and Computation 2(1): 31-50, 1992.
3. BENTON, P.N., 'A mixed linear and non-linear logic: Proofs, terms and models', in Proceedings of Conference on Computer Science Logic, volume 933 of Lecture Notes in Computer Science, 1995.
4. BENTON, P. N., G. M. BIERMAN, and V. C. V. de PAIVA, 'Computational types from a logical perspective', Journal of Functional Programming 8(2): 177-193, 1998.
5. BIERMAN, G. M., 'What is a categorical model of intuitionistic linear logic?', in Proceedings of Second International Conference on Typed λ-calculi and applications, volume 902 of Lecture Notes in Computer Science, pages 78-93, 1995.
6. BIERMAN, G. M., and V. C.V. de PAIVA, 'Intuitionistic necessity revisited', In Proceedings of Logic at Work Conference. Amsterdam, Holland, December 1992.
7. BIERMAN, G. M., and V. C. V. de PAIVA, 'Yet another intuitionistic modal logic (abstract)', Bulletin of Symbolic Logic, 1(2): 226, 1995.
8. BIERMAN, G. M., and V. C. V. de PAIVA, 'Intuitionistic necessity revisited', Technical Report CSR-96-10, School of Computer Science, University of Birmingham, June 1996.
9. BULL, R., and K. SEGERBERG, 'Basic modal logic', in Handbook of Philosophical Logic, pages 1-89. D. Reidel, 1984.
10. CURRY, H. B., 'The elimination theorem when modality is present', Journal of Symbolic Logic 17(4): 249-265, 1957.
11. CURRY, H. B., Foundations of Mathematical Logic, McGraw-Hill, 1963.
12. Van DALEN, D., 'Intuitionistic logic', volume 3 of Handbook of Philosophical Logic, chapter 4, pages 225-339. Reidel, 1986.
13. DAVIES, R., and F. PFENNING, 'A modal analysis of staged computation', in Proceedings of Symposium on Principles of Programming Languages, pages 258-270, 1996.
14. EILENBERG, S., and G. M. KELLY, 'Closed categories', in Proceedings of Conference on Categorical Algebra, La Jolla, 1966.
15. FAIRTLOUGH, M., and M. MENDLER, 'An intuitionistic modal logic with applications to the formal verification of hardware', in Proceedings of Conference on Computer Science Logic, volume 933 of Lecture Notes in Computer Science, 1995.
16. FLAGG, R. C., 'Church's thesis is consistent with epistemic arithmetic', In Intensional Mathematics, 1985.
17. GALLIER, J., 'Constructive logics part I: A tutorial on proof systems and typed A-calculi', Theoretical Computer Science 110(2): 249-339, 1993.
18. GENTZEN, G., 'Investigations into logical deduction', in M.E. Szabo (ed.), The Collected Papers of Gerhard Gentzen, pages 68-131, North-Holland, 1969.
19. GHILARDI, S., andG. MELONI, 'Modal and tense predicate logic: models in presheaves and categorical conceptualization', in Categorical Algebra and its Applications, volume 1348 of Lecture Notes in Mathematics, pages 130-142, 1988.
20. GIRARD, J.-Y., 'Linear logic', Theoretical Computer Science 50: 1-101, 1987.
21. GIRARD, J.-Y., Y. LAFONT, and P. TAYLOR, Proofs and Types, volume 7 of Cambridge Tracts in Theoretical Computer Science, Cambridge University Press, 1989.
22. GORE, R. P., Cut-free Sequent and Tableau Systems for Propositional Normal Modal Logics, PhD thesis, Computer Laboratory, University of Cambridge, 1992. Available as Computer Laboratory Technical Report 257.
23. HOWARD, W. A., 'The formulae-as-types notion of construction', in J. R. Hindley and J. P. Seldin (eds.), To H.B. Curry: Essays on combinatory logic, lambda calculus and formalism, Academic Press, 1980.
24. LAMBEK, J., and P. J. SCOTT, Introduction to Higher Order Categorical Logic, volume 7 of Cambridge studies in advanced mathematics, Cambridge University Press, 1987.
25. MAC LANE, S., Categories for the Working Mathematician, volume 5 of Graduate Texts in Mathematics, Springer Verlag, 1971.
26. MARTINI, S., and A. MASINI, 'A computational interpretation of modal proofs', Technical Report TR-27/93, Dipartimento di informatica, Università di Pisa, November 1993.
27. MINTS, G.E., Selected Papers in Proof Theory, Bibliopolis, 1992.
28. MINTS, G.E., 'Linear lambda-terms and natural deduction', Studia Logica 60: 209-231, 1998.
29. MINTS, G. E., 'Normal deduction in the intuitionistic linear logic', Archive for Mathematical Logic 37(5-6): 415-426, 1998.
30. MOGGI, E., 'Notions of computation and monads', Information and Control 93(1): 55-92, 1991.
31. PITTS, A.M., 'Categorical logic', Technical Report 367, Computer Laboratory, University of Cambridge, May 1995.
32. PRAWITZ, D., Natural Deduction, volume 3 of Stockholm Studies in Philosophy, Almqvist and Wiksell, 1965.
33. PRAWITZ, D., 'Ideas and results in proof theory', In J. E.Fenstad (ed.), Proceedings of Second Scandinavian Logic Symposium, pages 235-307, 1971.
34. REYES, G.E., andH. ZOLFAGHARI, 'Topos-theoretic approaches to modalities', Technical Report 911-8, Université de Montréal, Québec, April 1991.
35. SATRE, T. W., 'Natural deduction rules for modal logics', Notre Dame Journal of Formal Logic 8(4): 461-475, October 1972.
36. SCHWICHTENBERG, H., 'Proof theory: Some applications of cut-elimination', in J. Barwise (ed.), Handbook of Mathematical Logic, chapter D.2, pages 867-896, North Holland, 1977.
37. SIMPSON, A., The Proof Theory and Semantics of Intuitionistic Modal Logics, PhD thesis, University of Edinburgh, December 1993.
38. STIRLING, C. P., 'Modal logics for communicating systems', Theoretical Computer Science 49: 311-347, 1987.