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Logical Predicates for Intuitionistic Linear Type Theories (1999)  (Make Corrections)  (5 citations)
Masahito Hasegawa
Proceedings of the 4th International Conference on Typed Lambda Calculi and Applications (TLCA'99)



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Abstract: We develop a notion of Kripke-like parameterized logical predicates for two fragments of intuitionistic linear logic (MILL and DILL) in terms of their category-theoretic models. Such logical predicates are derived from the categorical glueing construction combined with the free symmetric monoidal cocompletion. As applications, we obtain full completeness results of translations between linear type theories. (Update)

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.... predicates (unary logical relations) for linear logic, which were originally introduced for categorytheoretic models of linear logic [5]. In this note we present the proof in entirely syntactic manner, for making the presentation self contained and also easier to access...

...in our previous work on models of linear type theories can be derived within this axiomatics. 1 Introduction In the previous work [2, 3] we have considered a glueing construction for symmetric monoidal (closed) categories, for studying the logical predicates for models of...

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3:   Girard, J-Y. 1987. `Linear Logic'. In: Theoretical Computer Science 59, pp1-102.
2:   What is a categorical model of intuitionistic linear logic - Bierman - 1995
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BibTeX entry:   (Update)

Hasegawa, M. (1999) Logical predicates for intuitionistic linear type theories. In Typed Lambda Calculi and Applications (TLCA'99), Lecture Notes in Computer Science 1581. Springer-Verlag. http://citeseer.ist.psu.edu/hasegawa99logical.html   More

@inproceedings{ hasegawa99logical,
    author = "Masahito Hasegawa",
    title = "Logical Predicates for Intuitionistic Linear Type Theories",
    booktitle = "Proceedings of the 4th International Conference on Typed Lambda Calculi and Applications ({TLCA}'99)",
    publisher = "Springer-Verlag",
    series = "LNCS",
    volume = "1581",
    address = "L'Aquila, Italy",
    editor = "Jean-Yves Girard",
    pages = "198--212",
    year = "1999",
    url = "citeseer.ist.psu.edu/hasegawa99logical.html" }
Citations (may not include all citations):
562   Categories for the Working Mathematician (context) - Lane - 1971
242   Linear logic (context) - Girard - 1987
89   Calculi for interaction - Milner - 1996
77   Dual intuitionistic linear logic (context) - Barber, Plotkin - 1997
66   What is a categorical model of intuitionistic linear logic - Bierman - 1995
28   Notes on sconing and relators - Mitchell, Scedrov - 1992
19   First Order Linear Logic in Symmetric Monoidal Closed Catego.. (context) - Ambler - 1992
17   Linear lambda-calculus and categorical models revisited - Benton, Bierman et al. - 1993
13   From action calculi to linear logic - Barber, Gardner et al. - 1998
11   A universal property of the convolution monoidal structure (context) - Im, Kelly - 1986
11   Full Completeness for Models of Linear Logic (context) - Tan - 1997
9   Bilinear logic in algebra and linguistics (context) - Lambek - 1995
9   Elementary control structures (context) - Power - 1996
8   Models of Lambda Calculi and Linear Logic: Structural - Loader - 1994
8   the runtime complexity of type-directed unboxing - Garrigue, Minamide - 1998
6   Logical Predicates and Indeterminates (context) - Hermida - 1994
5   A characterization of lambda denability in categorical model.. (context) - Alimohamed - 1995
3   Categorical glueing and logical predicates for models of lin.. - Hasegawa - 1999
3   egories et Machines (context) - Lafont - 1988
3   A mixed linear non-linear logic: proofs (context) - Benton - 1995
2   Specication structures and propositions-as-types for concurr.. (context) - Abramsky, Gay et al. - 1996
1   auchli semantics (context) - Blute, Scott et al. - 1996



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