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Abstract: Linear Logic [4] has raised a lot of interest in computer research, especially because of its resource sensitive nature. One line of research studies proof construction procedures and their interpretation as computational models, in the "Logic Programming" tradition. An efficient proof search procedure, based on a proof normalization result called "Focusing", has been described in [2]. Focusing is described in terms of the sequent system of commutative Linear Logic, which it refines in two... (Update)
Context of citations to this paper: More
...1.2 Problems in the non commutative case Let us rst concentrate on the multiplicative fragment MNL, which contains the main diculties. In [3], Andreoli and the rst author showed that the focalization property in sequent calculus corresponds to a hereditary splitting lemma for...
...non determinism . This duality is also one of the basic assumption of the new Ludics programme launched, recently, by Girard [5] In [3] it has been showed that the non commutative re nement of the linear connectives preserves the focusing duality. All the NL connectives are...
Cited by: More
Proof Construction and Non-Commutativity: a Cluster Calculus - Faggian (2000) (Correct)
An Overview of Linear Logic Programming - Dale Miller Inria (Correct)
Linear Logic Programming with an Ordered Context - Polakow (2000) (Correct)
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0.1: The Logic of Linear Functors - Blute, Cockett (2002) (Correct)
0.1: Non-commutative logic III: focusing proofs - Maieli, Ruet (2000) (Correct)
0.1: A Topological Correctness Criterion for Multiplicative.. - Mellies (Correct)
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0.2: Abstract Interpretation of Linear Logic Programming - Andreoli, Castagnetti.. (1993) (Correct)
0.2: Tree Adjoining Grammars in Noncommutative Linear.. - Abrusci.. (1997) (Correct)
0.2: A New Correctness Criterion for Multiplicative Non Commutative.. - Maieli (2001) (Correct)
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4: Non-commutative logic I: The multiplicative fragment - Abrusci, Ruet - 1998
4: Logic programming with focusing proofs in linear logic - Andreoli - 1992
3: Non-commutative logic II : sequent calculus and phase semantics - Ruet - 1998
BibTeX entry: (Update)
J.-M. Andreoli and R. Maieli. Focusing and proof nets in linear and noncommutative logic. In Proc. Int. Conf. on Logic for Programming and Automated Reasoning. Springer LNAI 1581, 1999. http://citeseer.ist.psu.edu/andreoli99focusing.html More
@misc{ andreoli99focusing,
author = "J. Andreoli and R. Maieli",
title = "Focusing and proof nets in linear and noncommutative logic",
text = "J.-M. Andreoli and R. Maieli. Focusing and proof nets in linear and noncommutative
logic. In Proc. Int. Conf. on Logic for Programming and Automated Reasoning.
Springer LNAI 1581, 1999.",
year = "1999",
url = "citeseer.ist.psu.edu/andreoli99focusing.html" }
Citations (may not include all citations):982 Theoretical Computer Science (context) - Girard - 1987 ACM
340 Uniform proofs as a foundation for logic programming (context) - Miller, Nadathur et al. - 1991 ACM DBLP
257 Logic programming in a fragment of intuitionistic linear log.. - Hodas, Miller - 1994 ACM DBLP
142 Logic programming with focusing proofs in linear logic - Andreoli - 1992 DBLP
53 Lexical scoping as universal quantification - Miller - 1989
46 Forum: A multiple-conclusion specification logic - Miller - 1996
42 Non commutative logic I: the multiplicative fragment - Abrusci, Ruet - 1998
29 Non commutative logic II: Sequent calculus and phase semanti.. - Ruet - 1998
17 concurrent structured processes (context) - Andreoli, Pareschi et al. - 1990
10 the meaning of logical rules I: syntax vs (context) - Girard - 1998
9 Pomset logic: A non-commutative extension of classical linea.. (context) - Retor'e - 1997
1 Informal communication (context) - Girard
Documents on the same site (http://iml.univ-mrs.fr/~maieli/papers.html):
A New Correctness Criterion for Multiplicative Non Commutative.. - Maieli (2001) (Correct)
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