A Noncommutative Full Completeness Theorem (Extended Abstract) (1996)
| Venue: | Elsevier Science B.V |
| Citations: | 1 - 1 self |
BibTeX
@INPROCEEDINGS{Blute96anoncommutative,
author = {R. F. Blute and P. J. Scott},
title = {A Noncommutative Full Completeness Theorem (Extended Abstract)},
booktitle = {Elsevier Science B.V},
year = {1996}
}
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Abstract
) R.F. Blute 1 P.J. Scott 1 Dept. of Mathematics University of Ottawa Ottawa, Ontario K1N 6N5 CANADA E. N. T. C. S. Elsevier Science B. V. Abstract We present a full completeness theorem for the multiplicative fragment of a variant of noncommutative linear logic known as cyclic linear logic (CyLL), first defined by Yetter. The semantics is obtained by considering dinatural transformations on a category of topological vector spaces which are invariant under certain actions of a noncocommutative Hopf algebra, called the shuffle algebra. Multiplicative sequents are assigned a vector space of such dinaturals, and we show that the space has the denotations of cut-free proofs in CyLL+MIX as a basis. This work is a natural extension of the authors' previous work, "Linear Lauchli Semantics", where a similar theorem is obtained for the commutative logic. In that paper, we consider dinaturals which are invariant under certain actions of the additive group of integers. The passage from group...
