Propositional Lax Logic

Information and Computation

Volumn 137, Issue 1, 1997, Pages 1-33

  Fairtlough, Matt ^a   Mendler, Michael ^b  

^a UNIVERSITY OF SHEFFIELD   (United Kingdom)

^b UNIVERSITY OF PASSAU   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0001830019     PISSN: 08905401     EISSN: None     Source Type: Journal    
DOI: 10.1006/inco.1997.2627     Document Type: Article

References (31)

1. Avellone, A., and Ferrari, M. (1996), Almost duplication-free tableau calculi for prepositional lax logics, in "Proceedings of the 5th International Workshop on Theorem Proving with Analytic Tableaux and Related Methods" (P. Miglioli, U. Moscato, D. Mundici, and M. Ornaghi, Eds.), Lecture Notes in Artificial Intelligence, Vol. 1071, Springer-Verlag, Berlin/New York.
2. Baccelli, F., Cohen, G., Olsder, G. J., and Quadrat, J.-P. (1992), "Synchronization and Linearity," Wiley, New York.
3. Benton, N., Bierman, G., and de Paiva, V. (1995), "Computational Types from a Logical Perspective, I," Technical Report 365, University of Cambridge Computer Laboratory.
4. Chellas, B. (1980), "Modal Logic," Cambridge Univ. Press, Cambridge, UK.
5. Curry, H. B. (1952), The elimination theorem when modality is present, J. Symbolic Logic 17, 249-265.
6. Curry, H. B. (1957), "A Theory of Formal Deducibility," Notre Dame Mathematical Lectures, 2nd ed., Vol. 6, Notre Dame, IN.
7. Dummett, M. (1977), "Elements of Intuitionism," Clarendon Press, Oxford.
8. Ewald, W. B. (1986), Intuitionistic tense and modal logic, J. Symbolic Logic 51, 166-179.
9. Fischer-Servi, G. (1980), Semantics for a class of intuitionistic modal calculi, in "Italian Studies in the Philosophy of Science" (M. L. D. Chiara, Ed.), pp. 59-72, Reidel, Dordrecht.
10. Fitting, M. (1983), "Proof Methods for Modal and Intuitionistic Logics," Reidel, Dordrecht.
11. Gabbay, D. M., and DeJongh, D. H. J. (1975), A sequence of decidable finitely axiomatizable intermediate logics with the disjunction property, J. Symbolic Logic 39(1), 67-78.
12. Gödel, K. (1932), Zum intuitionistischen Aussagenkalkül, Akad. Wissenschaften Wien Math.-Naturwiss. Klasse Anzeiger. 69, 65-66.
13. Goldblatt, R. I. (1979), "Topoi: The Categorial Analysis of Logic," Studies in Logic and the Foundations of Mathematics, Vol. 97, North-Holland, Amsterdam.
14. Goldblatt, R. I. (1981), Grothendieck topology as geometric modality, Z. Math. Logik Grundlag. Math. 27, 495-529.
15. Johansson, I. (1936), Der Minimalkalkül, ein reduzierter intuitionistischer Formalismus, Compositio Math. 4, 119-136.
16. Kreisel, G., and Putnam, H. (1957), Eine Unableitbarkeitsbeweismethode für den intuitionistischen Aussagenkalkül, Arch. Math. Logik Grundlagenforsch. 3, 74-78.
17. Macnab, D. S. (1981), Modal operators on Heyting algebras, Algebra Universalis 12, 5-29.
18. Maksimova, L. L. (1986), On maximal intermediate logics with the disjunction property, Studia Logica 45, 69-75.
19. Medvedev, J. T. (1966), Interpretation of logical formulas by means of finite problems, Sov. Math. Dokl. 7(4), 857-860.
20. Mendler, M. (1990), Constrained proofs: A logic for dealing with behavioural constraints in formal hardware verification, in "Designing Correct Circuits (DCC '90)" (G. Jones and M. Sheeran, Eds.), pp. 1-28, Springer-Verlag, Berlin/New York.
21. Mendler, M. (1993), "A Modal Logic for Handling Behavioural Constraints in Formal Hardware Verification," Ph.D. thesis, Department of Computer Science, ECS-LFCS-93-255, Edinburgh University.
22. Mendler, M. (1996), Timing refinement of intuitionistic proofs and its application to the timing analysis of combinatorial circuits, in "Proceedings of the 5th International Workshop on Theorem Proving with Analytic Tableaux and Related Methods" (P. Miglioli, U. Moscato, D. Mundici, and M. Ornaghi, Eds.), Lecture Notes in Artificial Intelligence, Vol. 1071, pp. 261-277, Springer-Verlag, Berlin/New York.
23. MendLer, M., and Fairtlough, M. (1996), Ternary simulation: A refinement of binary functions or an abstraction of real-time behaviour?, in "Proceedings of the 3rd Workshop on Designing Correct Circuits (DCC '96), Båstad, Sweden" (M. Sheeran and S. Singh, Eds.), Electronic Workshops in Computing, Springer-Verlag, Berlin/New York.
24. Miglioli, P., Moscato, U., Ornaghi, M., Quazza, S., and Usberti, G. (1989), Some results on intermediate constructive logics, Notre Dame J. Formal Logic 30(4), 543-562.
25. Moggi, E. (1991), Notions of computation and monads, Inform. and Comput. 93, 55-92.
26. Plotkin, G., and Stirling, C. (1986), A framework for intuitionistic modal logics, in "Theoretical Aspects of Reasoning about Knowledge," pp. 399-406, Monterey.
27. Popkorn, S. (1994), "First Steps in Modal Logic," Cambridge Univ. Press, Cambridge, UK.
28. Simmons, H. (1989), A framework for topology, in "Logic Colloqium "77" (A. Macintyre, L. Pacholski, and J. Paris, Eds.), pp. 239-251, North-Holland, Amsterdam.
29. Simpson, A. (1994), "The Proof Theory and Semantics of Intuitionistic Modal Logic," Ph.D. thesis, Univ. of Edinburgh, Department of Computer Science.
30. Thompson, S. (1996), "Haskell - The Craft of Functional Programming," Addison-Wesley, Reading, MA.
31. Troelstra, A. S., and van Dalen, D. (1988), "Constructivism in Mathematics," Vol. II, North-Holland, Amsterdam.