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Fuzzy models of linear logic

Published online by Cambridge University Press:  04 March 2009

Michael Barr
Michael Barr
Affiliation:
Department of Mathematics and Statistics, 805 Sherbrooke St. W., McGill University, Montreal, Quebec H3A 2K6, Canada Email: barr@math.mcgill.ca
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Abstract

It is shown that the category of fuzzy relations with values in a ∗-autonomous poset gives a ∗-autonomous category. It is also shown that this construction can be generalized by replacing the ∗-autonomous poset by a ∗-autonomous category. In both cases, cofree coalgebras exist so that there is a natural! operation.

Type
Research Article
Information
Mathematical Structures in Computer Science , Volume 6 , Issue 3 , June 1996 , pp. 301 - 312
Copyright
Copyright © Cambridge University Press 1996

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References

Barr, M. (1979) *-Autonomous categories. Springer-Verlag Lecture Notes in Mathematics 752.CrossRefGoogle Scholar
Barr, M. (1991) *-Autonomous categories and linear logic. Mathematical Structures in Computer Science 1 159–178.CrossRefGoogle Scholar
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 45–65. (Expanded version to appear in Journal of Pure and Applied Algebra.)Google Scholar