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Abstract: We present a sequent calculus for non-commutative logic which enjoys the focalization property. In the multiplicative case, we give a focalized sequentialization theorem, and in the general case, we show that our focalized sequent calculus is equivalent to the original one by studying the permutabilities of rules for NL and showing that all LL permutabilities involved in focalization can be lifted to NL permutabilities. These results are based on a study of the partitions of partially... (Update)
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BibTeX entry: (Update)
R. Maieli and P. Ruet. Non commutative logic III: focusing proofs. Technical Report 2000-14, insitut de Mathematiques de Luminy, 2000. http://citeseer.ist.psu.edu/maieli00noncommutative.html More
@misc{ maieli00non,
author = "R. Maieli and P. Ruet",
title = "Non commutative logic III: focusing proofs",
text = "R. Maieli and P. Ruet. Non commutative logic III: focusing proofs. Technical
Report 2000-14, insitut de Mathematiques de Luminy, 2000.",
year = "2000",
url = "citeseer.ist.psu.edu/maieli00noncommutative.html" }
Citations (may not include all citations):340 Uniform proofs as a foundation for logic programming (context) - Miller, Nadathur et al. - 1991
248 The mathematics of sentence structure (context) - Lambek - 1958
242 Linear logic (context) - Girard - 1987
223 Linear objects: logical processes with built-in inheritance - Andreoli, Pareschi - 1991
142 Logic programming with focusing proofs in linear logic - Andreoli - 1992
42 Non-commutative logic I: the multiplicative fragment - Abrusci, Ruet - 2000
38 On proof normalization in linear logic - Galmiche, Perrier - 1994
31 Computationally tractable classes of ordered sets (context) - Mohring - 1989
29 Non-commutative logic II: sequent calculus and phase semanti.. - Ruet - 2000
10 the meaning of logical rules I: syntax vs (context) - Girard - 1999
7 Proof search in rst-order linear logic and other cut-free se.. (context) - Lincoln, Shankar - 1994
5 Focusing and proof nets in linear and noncommutative logic - Andreoli, Maieli - 1999
3 the meaning of logical rules II: multiplicative / additive c.. (context) - Girard - 2000
1 Preprint Institut de Mathematiques de Luminy (context) - Girard - 2000
1 Focusing full non-commutative sequent calculus (context) - Maieli - 2000
Documents on the same site (http://iml.univ-mrs.fr/~ruet/): More
Non-commutative logic I: the multiplicative fragment - Abrusci, Ruet (1998) (Correct)
Hopf Algebras and Models of Non-commutative Logic - Blute, Ruet (2000) (Correct)
Non-commutative logic II: sequent calculus and phase semantics - Ruet (1998) (Correct)
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