(Enter summary)
Abstract: We introduce a new category of finite, fair games, and winning strategies, and use it to provide
a semantics for the multiplicative fragment of Linear Logic (mll) in which formulae are interpreted
as games, and proofs as winning strategies. This interpretation provides a categorical model of mll
which satisfies the property that every (history-free, uniformly) winning strategy is the denotation
of a unique cut-free proof net. Abramsky and Jagadeesan first proved a result of this kind and
they... (Update)
Context of citations to this paper: More
...by most naturally arising models of linear logic, is nevertheless omitted from pure linear logic. Seeking the real McCoy, Hyland and Ong [6] modify AJ s model to refute MIX by disallowing certain plays they characterize as unfair. This work was supported by ONR under grant...
.... have since been verified as canonical from a semantic perspective, with numerous full completeness results for MLL, e.g. [AJ94, HO93, Loa94, Tan97, BS96, DHPP99]. Furthermore, the identifications correspond to coherences of free star autonomous categories [BCST96] The problem...
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31: Games and full completeness for multiplicative linear logic
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15: Theoretical Computer Science (context) - Girard - 1987
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BibTeX entry: (Update)
J.M.E. Hyland and C.-H.L. Ong. Fair games and full completeness for multiplicative linear logic without the mix-rule. Available by ftp from ftp.comlab.ox.ac.uk as fcomplete.ps.gz in /pub/Documents/techpapers/Luke.Ong, 1993. http://citeseer.ist.psu.edu/hyland93fair.html More
@unpublished{ hyland93fair,
author = "J. M. E. Hyland and C.-H. L. Ong",
title = "Fair Games and Full Completeness for Multiplicative Linear Logic without the Mix-Rule",
year = "1993",
url = "citeseer.ist.psu.edu/hyland93fair.html" }
Citations (may not include all citations):
982
Theoretical Computer Science (context) - Girard - 1987
175
Games and Full Completeness for Multiplicative Linear Logic
- Abramsky, Jagadeesan - 1992
103
On Numbers and Games (context) - Conway - 1976
72
Archive for Mathematical Logic (context) - Danos, Regnier et al. - 1989
49
Annals of Pure and Applied Logic (context) - Blass, semantics et al. - 1992
43
Games semantics for linear logic (context) - Lafont, Streicher - 1991
32
Mathematical Structures in Computer Science (context) - Barr, categories et al. - 1991
22
Concurrency on automata and infinite sequences (context) - Park - 1981
13
Proof nets for multiplicative and additive linear logic (context) - Bellin - 1993
12
Fundamentals of Contemporary Set Theory (context) - Devlin - 1980
10
Remarques sur la theorie des jeux a deux personnes (context) - Joyal - 1977
5
Progress in Theoretical Computer Science Series (context) - Curien, Sequential et al. - 1993
5
Lecture Notes in Mathematics Vol (context) - Barr, categories - 1979
5
CSLI Lecture Notes No (context) - Troelstra, Linear et al. - 1992
4
Conway games and linear logic (context) - Hyland - 1990
2
cofree algebras and linear logic (context) - Seely, categories - 1989
1
the proof net problem for additives in linear logic (context) - Lamarche - 1993
1
On fair games and parallelism (context) - Huth - 1993
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