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Abstract: We investigate the linear logic of Chu spaces as defined by its dinaturality semantics. For those formulas of multiplicative linear logic limited to at most two occurrences of each variable we prove full completeness of Girard's MIX-free axiomatization, namely that the cut-free proofnets of such formulas are in a natural bijection with the dinatural elements of the corresponding functors. 1 Introduction Whereas ordinary logic axiomatizes theorems, linear logic axiomatizes proofs. The semantic... (Update)
Context of citations to this paper: More
...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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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/article/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/article/pratt97towards.html" }
Citations (may not include all citations):982 Theoretical Computer Science (context) - Girard - 1987
562 Categories for the Working Mathematician (context) - Lane - 1971
359 Introduction to Higher-Order Categorical Logic (context) - Lambek, Scott - 1986
175 Games and full completeness for multiplicative linear logic - Abramsky, Jagadeesan - 1994
72 Archive for Mathematical Logic (context) - Danos, Regnier et al. - 1989
43 Games semantics for linear logic (context) - Lafont, Streicher - 1991
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
24 The Stone gamut: A coordinatization of mathematics - Pratt - 1995
16 Annals of Pure and Applied Logic (context) - Blute, Scott et al. - 1996
7 The shuffle Hopf algebra and noncommutative full completenes.. - Blute, Scott - 1996
4 Broadening the denotational semantics of linear logic - Pratt - 1996
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