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Abstract: The paper studies the properties of the subnets of proof-nets. Very simple proofs are obtained of known results on proof-nets for MLL \Gamma , Multiplicative Linear Logic without propositional constants. Contents 1 Preface 1 2 Proof Nets for Propositional MLL \Gamma 3 2.1 Propositional Proof Structures and Proof Nets : : : : : : : : : : 3 2.2 Subnets : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 5 2.3 Empires and Kingdoms: Existence and Properties : : : : : : : : 8 2.4... (Update)
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...the formulae labelling the nodes and only represents the connectives. Here we recall the inductive definition of proof net, introduced by Bellin [5]. Definition 20 A MLL proof net and its set of conclusions are inductively defined in the following way: If A is any...
...L j iff c i 2 oe (a j ; b j ) a i b i = oe(L i ) c i a j = oe(L j ) b j Lemma 5.4 The relation OE oe is well founded. Upsilon In [BW95] the difficulty is to prove the existence of the empire; in our approach the problem is turned into showing non triviality of the empire of...
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BibTeX entry: (Update)
G. Bellin and J. van de Wiele. Subnets of proof-nets in MLL . In J.Y. Girard, Y. Lafont, and L. Regnier, editors, Advances in Linear Logic, pages 249--260. Cambridge University Press, 1995. http://citeseer.ist.psu.edu/bellin94subnets.html More
@misc{ bellin95subnets,
author = "G. Bellin and J. Wiele",
title = "Subnets of proof-nets in MLL",
text = "G. Bellin and J. van de Wiele. Subnets of proof-nets in MLL . In J.Y. Girard,
Y. Lafont, and L. Regnier, editors, Advances in Linear Logic, pages 249--260.
Cambridge University Press, 1995.",
year = "1995",
url = "citeseer.ist.psu.edu/bellin94subnets.html" }
Citations (may not include all citations):982 Theoretical Computer Science (context) - Girard - 1987
16 Mechanizing Proof Theory: Resource-Aware Logics and ProofTra.. (context) - Bellin - 1990
13 Proof Nets for Multiplicative and Additive Linear Logic (context) - Bellin - 1991
13 Part II: Linear Logic and Proof Nets (context) - Gallier
4 Quantifiers in Linear Logic (context) - Girard - 1987
1 Subnets of proof-nets in MLL \Gamma (context) - Danos, Regnier et al. - 1989
1 Gianluigi Bellin and Jacques van de Wiele (context) - Girard, linear et al.
Documents on the same site (http://www.amsta.leeds.ac.uk/~bellin/papers.html):
Planar and Braided Proof-Nets for Multiplicative Linear Logic .. - Bellin, Fleury (1997) (Correct)
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