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Abstract: Completeness is shown for several versions of Girard's linear logic with respect to Petri nets as the class of models. The strongest logic considered is intuitionistic linear logic, with\Omega , (, & , \Phi and the exponential ! ("of course"), and forms of quantification. This logic is shown sound and complete with respect to atomic nets (these include nets in which every transition leads to a nonempty multiset of places). The logic is remarkably expressive, enabling descriptions of the kinds... (Update)
Context of citations to this paper: More
.... consider BI s use as a basis for a range of models in which the notion of resource is concrete: Petri nets: classical true concurrency [15]; Ambient logic: mobile processes [8] Memory allocation and deallocation: a basic separation model [46, 22] 13 . Pointer logic:...
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17: Theoretical Computer Science (context) - Girard - 1987
9: The semantics and proof theory of the logic of bunched implications (context) - Pym - 1998
8: Petri nets as models of linear logic - Engberg, Winskel - 1990
BibTeX entry: (Update)
U. Engberg and G. Winskel. Completeness results for linear logic on Petri nets. In A. Borzyszkowski and S. Soko/lowski, editors, Mathematical Foundations of Computer Science (MFCS'93), number 711 in LNCS, pages 442--452, Gda'nsk, Poland, Aug. 1993. Full version is DAIMI PB, Jan. 1993. http://citeseer.ist.psu.edu/engberg93completeness.html More
@inproceedings{ engberg93completeness,
author = "U. Engberg and G. Winskel",
title = "Completeness Results for Linear Logic on {Petri} Nets",
booktitle = "Proceedings of the Conference on Mathematical Foundations of Computer Science",
publisher = "Springer-Verlag LNCS 711",
address = "Gda{\'n}sk, Poland",
editor = "A. Borzyszkowski and S. Sokolowski",
pages = "442--452",
year = "1993",
url = "citeseer.ist.psu.edu/engberg93completeness.html" }
Citations (may not include all citations):215 Theoretical Computer Science (context) - Lafont, Abstract - 1988
215 Theoretical Computer Science (context) - Girard - 1987
87 volume 4 of EATCS Monographs on Theoretical Computer Science (context) - Reisig, An - 1985
37 The Journal of Symbolic Logic (context) - Yetter, Non-Commutative et al. - 1990
15 Relating Petri Nets to Formulae of Linear Logic (context) - Brown - 1989
6 Linear Logic and Lazy Computation (context) - Girard, Lafont - 1987
4 Notes by Steve Vickers (context) - Abramsky, Vickers et al. - 1988
4 Manuscript reported to us by Per Martin-Lof (context) - Sambin
4 Technical Report MS-CIS (context) - Gunter, Gehlot et al. - 1989
4 A Note on Girard Quantales (context) - Rosenthal - 1990
3 Petri Nets as Models of Linear Logic - Engberg, Winskel - 1990
3 From Petri Nets to Linear Logic: a Survey (context) - Mart'i-Oliet, Meseguer - 1991
The graph only includes citing articles where the year of publication is known.
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