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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 equivariant 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... (Update)
Context of citations to this paper: More
...by a formula is required to be universally true. Following Lambek and Scott [11] and (as applied to linear logic) Blute and Scott [3, 4], we shall take the semantic criterion for proofhood to be naturality: the transformation denoted by a proof is required to commute with all...
.... we hope to take advantage of the fact that distributions form a D module, that is to say they provide representations of the Weyl algebra [20] It would be interesting to attempt to extend the work of [16, 17], where full completeness theorems are obtained by considering...
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BibTeX entry: (Update)
R.F. Blute and P.J. Scott. The shuffle Hopf algebra and noncommutative full completeness. Submitted to J. Symbolic Logic, 1996. http://citeseer.ist.psu.edu/blute96shuffle.html More
@article{ blute96shuffle,
author = "R. F. Blute and P. J. Scott",
title = "The shuffle {Hopf} algebra and noncommutative full completeness",
journal = "Submitted to J. Symbolic Logic",
year = "1996",
url = "citeseer.ist.psu.edu/blute96shuffle.html" }
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982 Theoretical Computer Science (context) - Blute, Logic et al. - 1993 ACM
175 Games and Full Completeness for Multiplicative Linear Logic - Abramsky, Jagadeesan - 1994 ACM DBLP
63 Theoretical Computer Science (context) - Bainbridge, Freyd et al. - 1990
54 Phase Semantics and Sequent Calculus for Pure Noncommutative.. (context) - Abrusci - 1991
51 Une Th'eorie Combinatoire des S'eries formelles (context) - Joyal - 1981
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19 Cambridge University Press (context) - Ab'e, Algebras - 1977
17 Quasitriangular Hopf Algebras and Yang-Baxter Equations (context) - Majid - 1990
16 Annals of Pure and Applied Logic (context) - Blute, Scott et al. - 1996
16 Antipodes and Incidence Coalgebras (context) - Schmitt - 1987 ACM
11 Mathematical Structures in Computer Science (context) - Blute, Algebras et al. - 1996
9 Bilinear Logic in Algebra and Linguistics (context) - Lambek - 1993 ACM
9 Springer Lecture Notes in Mathematics (context) - Barr, Categories - 1980
7 Studies in Applied Mathematics (context) - Joni, Rota et al. - 1979
7 An Abstract Notion of Realizability for which Intuitionistic.. (context) - Lauchli - 1970
7 Normal Forms and Cut-free Proofs as Natural Transformations - Girard, Scedrov et al. - 1991
7 Bialgebras: Some Foundations for Distributed and Concurrent .. (context) - Benson - 1989
6 American Mathematical Society Colloquium Publications (context) - Lefschetz, Topology - 1963
5 Physics for Algebraists: Noncommutative and Noncocommutative.. (context) - Majid - 1990
5 Autonomous Categories of Bimodules (context) - Rosenthal - 1994
4 private communication (context) - Plotkin - 1996
4 Duality of Vector Spaces (context) - Barr - 1976
4 Lambek's Categorical Proof Theory and Lauchli's Abstract Rea.. (context) - Harnik, Makkai - 1992
4 Introductory Recommendations for the Study of Hopf Algebras .. (context) - Hazewinkel - 1991
4 On Hopf Algebras and Rigid Monoidal Categories (context) - Ulbrich - 1989
4 Benjamin Press (context) - Sweedler, Algebras - 1969
3 Hopf Algebras of Combinatorial Structures (context) - Schmitt - 1993
2 Duality of Banach Spaces (context) - Barr - 1976
2 Appendix to (context) - Barr - 1994
2 Des R'eseaux De D'emonstration Pour La Linguistique (context) - Retor'e - 1996
2 Springer Lecture Notes in Computer Science (context) - Plotkin, Abadi et al. - 1993
1 and lectures delived at Keio University (context) - Girard, Spaces - 1996
1 Electronic Notes in Theoretical Computer Science (context) - Blute, Scott et al. - 1996
1 Noncommutative -autonomous Categories (context) - Barr - 1993
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