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Fair Games and Full Completeness for Multiplicative Linear Logic without the MIX-Rule (1993)  (Make Corrections)  (29 citations)
J.M.E. Hyland, C.-H.L. Ong



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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)

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...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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Concurrent Games and Full Completeness - Samson Abramsky Lfcs (1998)   (Correct)
Proof Nets for Unit-free Multiplicative-Additive Linear Logic - Extended Dominic (2003)   (Correct)
Games in the Semantics of Programming Languages - An Elementary.. - Jürjens (1999)   (Correct)

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0.7:   Explicit Substitution Internal Languages for Autonomous and.. - Koh, Ong (1999)   (Correct)
0.4:   Games and Full Completeness for Multiplicative Linear Logic - Abramsky, Jagadeesan (1994)   (Correct)
0.2:   Correspondence between operational and denotational semantics: the.. - Ong (1995)   (Correct)

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31:   Games and full completeness for multiplicative linear logic - Abramsky, Jagadeesan - 1994
15:   Theoretical Computer Science (context) - Girard - 1987
12:   Annals of Pure and Applied Logic (context) - Blass, semantics et al. - 1992

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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