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! and ? – Storage as tensorial strength

  • R. F. Blute (a1), J. R. B. Cockett (a2) and R. A. G. Seely (a3)

Abstract

We continue our study of the negation-free structure of multiplicative linear logic, as represented by the structure of weakly distributive categories, to consider the ‘exponentials’! and ? in the weakly distributive context. In addition to the usual triple and cotriple structure that one would expect on each of the two operators, there must be some connection between them to replace the de Morgan relationship found in the linear logic context. This turns out to be the notion of tensorial strength. We analyze coherence for this situation, using a modification of the usual nets due to Danos, which is a form suitable for linear logic with exponentials but without negation.

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Barr, M. (1991) *-Autonomous categories and linear logic. Math. Struct, in Comp. Science 1 159178.
Benton, B. N., Bierman, G., de Paiva, V., AND Hyland, M., (1992) Term assignment for intuitionistic linear logic (preliminary report). Technical Report 262, University of Cambridge.
Bierman, G. M. (1995) What is a categorical model of intuitionistic linear logic?. In: Dezani, M., (ed.) Proceedings of Conference on Typed lambda calculus and Applications, Springer-Verlag. (Also: Technical Report 333, University of Cambridge, 1994.)
Blute, R. F. (1995) Linear Logic, Coherence and Dinaturality. Theoretical Computer Science 115 341.
Blute, R., Cockett, J. R. B., Seely, R. A. G. and Trimble, T. H. (1992) Natural deduction and coherence for weakly distributive categories. To appear in Journal of Pure and Applied Algebra. (Also: Preprint, McGill University, 1992, revised 1994.)
Cockett, J. R. B. (1995) Introduction to distributive categories. Math. Struct. in Comp. Science 3 277308.
Cockett, J. R. B. and Seely, R. A. G. (1992) Weakly distributive categories. In: Fourman, M. P., Johnstone, P. T. and Pitts, A. M. (eds.) Applications of Categories to Computer Science, London Mathematical Society Lecture Note Series 177 4565. (Expanded version to appear in Journal of Pure and Applied Algebra.)
Cockett, J. R. B. and Seely, R. A. G. (1995) Proof theory for linear logics without negation. Preprint, McGill University.
Danos, V., (1990) La logique linéaire appliquée à l’étude de divers processus de normalisation et principalement du λ-calcul, Doctoral dissertation, Université de Paris.
Danos, V., AND Regnier, L., (1989) The structure of multiplicatives. Archive for Math. Logic 28 181203.
Fox, T., (1976) Coalgebras and Cartesian categories. Communications in Algebra 7 665667.
Girard, J.-Y. (1987) Linear logic. Theoretical Computer Science 50 1102.
Girard, J.-Y. (1991) A new constructive logic: classical logic. Math. Struct. in Comp. Science 1 255296.
Joyal, A., AND Street, R., (1991) The geometry of tensor calculus I. Advances in Mathematics 88 55112.
Lambek, J., (1969) Deductive systems and categories II. Springer-Verlag Lecture Notes in Mathematics 87.
Lincoln, P., AND Winkler, I., (1994) Constant-only multiplicative linear logic is NP-complete. Theoretical Computer Science 135 155169.
Prawitz, D., (1965) Natural Deduction, Almqvist and Wiksell, Uppsala.
Seely, R. A. G. (1989) Linear logic, *-autonomous categories and cofree coalgebras. In: Gray, J., AND Scedrov, A. (eds.) Categories in Computer Science and Logic Contemporary Mathematics 92 Am. Math. Soc.
Trimble, T. H. (1994) Linear logic, bimodules, and full coherence for autonomous categories, Doctoral dissertation, Rutgers University.

! and ? – Storage as tensorial strength

  • R. F. Blute (a1), J. R. B. Cockett (a2) and R. A. G. Seely (a3)

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