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! and ? – Storage as tensorial strength

Published online by Cambridge University Press:  04 March 2009

R. F. Blute ,
J. R. B. Cockett  and
R. A. G. Seely
R. F. Blute
Affiliation:
Department of Mathematics, University of Ottawa, 585 King Edward St., Ottawa, ON, K1N6N5, Canada. Email [email protected]. ca
J. R. B. Cockett
Affiliation:
Department of Computer Science, University of Calgary, 2500 University Drive, Calgary, AL, T2N 1N4, Canada. Email robin@cpsc. ucalgary. Ca
R. A. G. Seely
Affiliation:
Department of Mathematics, McGill University, 805 Sherbrooke St., Montréal, PQ, H3A 2K6, Canada. Email [email protected]
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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.

Type
Research Article
Information
Mathematical Structures in Computer Science , Volume 6 , Issue 4 , August 1996 , pp. 313 - 351
Copyright
Copyright © Cambridge University Press 1996

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