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Abstract: We prove full completeness for a fragment of the linear logic of the self-dual monoidal category of Chu spaces over 2, namely that the proofs between semisimple (conjunctive normal form) formulas of multiplicative linear logic without constants having two occurrences of each variable are in bijection with the dinatural transformations between the corresponding functors. The proof assigns to variables domains having at most four elements, demonstrating a uniform finite model property for... (Update)
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...science in general which is promoted by V. R. Pratt from Stanford under the name of Chu spaces (see, e. g, [5, 6, 7, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23]) Thus, a general extension of t norms naturally leads us to Chu spaces. Auxiliary Results and Their...
...However linear logic contains functors of mixed variance 1 such as A GammaffiA, for which mere naturality is not enough. Elsewhere [Pra97] we have shown that when the morphisms are taken to be ordinary dinatural transformations, as done by Blute and Scott [BS96a, BS96b]...
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5: The Stone Gamut: A Coordinatization of Mathematics - Pratt - 1995
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BibTeX entry: (Update)
V. R. Pratt, "Towards Full Completeness of the Linear Logic of Chu Spaces", Electronic Notes in Theoretical Computer Science, 1997, Vol. 6 (http://www.elsevier.nl/locate/entcs/volume6.html). http://citeseer.ist.psu.edu/pratt97towards.html More
@inproceedings{ pratt97towards,
author = "V. R. Pratt",
title = "Towards Full Completeness for the Linear Logic of Chu Spaces",
booktitle = "Preliminary Proceedings of the 13th Annual Conference on Mathematical Foundations of Programming Semantics",
address = "Pittsburgh",
year = "1997",
url = "citeseer.ist.psu.edu/pratt97towards.html" }
Citations (may not include all citations):175 Games and full completeness for multiplicative linear logic - Abramsky, Jagadeesan - 1994 ACM DBLP
42 volume 752 of Lecture Notes in Mathematics (context) - Barr, categories - 1979
36 Chu Spaces: A Model of Concurrency - Gupta - 1994
31 Gates accept concurrent behavior - Gupta, Pratt - 1993
29 Fair games and full completeness for multiplicative linear l.. - Hyland, Ong - 1993
27 Chu spaces and their interpretation as concurrent objects - Pratt - 1995 DBLP
24 The Stone gamut: A coordinatization of mathematics - Pratt - 1995 DBLP
12 The finite model property for various fragments of linear lo.. - Lafont - 1996 DBLP
11 Mathematical Structures in Computer Science (context) - Blute, linear et al. - 1996
4 Broadening the denotational semantics of linear logic - Pratt - 1996 DBLP
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