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Abstract: We introduce a new correctness criterion for multiplicative non commutative proof nets which can be considered as the non-commutative counterpart to the Danos-Regnier criterion for proof nets of linear logic. The main intuition relies on the fact that any switching for a proof net (obtained by mutilating one premise of each disjunction link) can be naturally viewed as a series-parallel order variety (a cyclic relation) on the conclusions of the proof net. 1. (Update)
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A Topological Correctness Criterion for Multiplicative.. - Mellies (Correct)
Quadratic correctness criterion for Non commutative Logic - Virgile Mogbil Institut (2001) (Correct)
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0.0: Non-commutative logic III: focusing proofs - Maieli, Ruet (2000) (Correct)
0.0: A System of Interaction and Structure - Guglielmi (2002) (Correct)
0.0: Proof Construction and Non-Commutativity: a Cluster Calculus - Faggian (2000) (Correct)
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0.6: Non-commutative logic II: sequent calculus and phase semantics - Ruet (1998) (Correct)
0.6: Non-commutative logic I: the multiplicative fragment - Abrusci, Ruet (1998) (Correct)
0.6: Focusing Non-commutative Sequent Calculus - Maieli (2000) (Correct)
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2: Towards a geometry of interaction (context) - Girard - 1989
2: Non-commutative logic I: The multiplicative fragment - Abrusci, Ruet - 1998
2: Non-commutative logic II : sequent calculus and phase semantics - Ruet - 1998
BibTeX entry: (Update)
R. Maieli. A new correctness criterion for multiplicative noncommutative proof-nets. Technical report, Institut de mathematiques de Luminy, 2000. http://citeseer.ist.psu.edu/maieli01new.html More
@misc{ maieli00new,
author = "R. Maieli",
title = "A new correctness criterion for multiplicative noncommutative proof-nets",
text = "R. Maieli. A new correctness criterion for multiplicative noncommutative
proof-nets. Technical report, Institut de mathematiques de Luminy, 2000.",
year = "2000",
url = "citeseer.ist.psu.edu/maieli01new.html" }
Citations (may not include all citations):248 The mathematics of sentence structure (context) - Lambek - 1958
242 Linear logic (context) - Girard - 1987
42 Non-commutative logic I: the multiplicative fragment - Abrusci, Ruet - 2000
31 The structure of multiplicatives (context) - Danos, Regnier - 1989
31 Computationally tractable classes of ordered sets (context) - Mohring - 1989
29 Non-commutative logic II: sequent calculus and phase semanti.. - Ruet - 2000
1 Imagine to cut a proof net and obtain two (context) - Yetter, non-commutative et al. - 1990
1 Modules in non-commutative logic (context) - Abrusci - 1999
Documents on the same site (http://iml.univ-mrs.fr/~maieli/papers.html):
Focusing and Proof-Nets in Linear and Non-Commutative Logic - Andreoli, Maieli (1999) (Correct)
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