Connection-based proof construction in Non-Commutative Logic
Identifieur interne : 003944 ( Crin/Curation ); précédent : 003943; suivant : 003945Connection-based proof construction in Non-Commutative Logic
Auteurs : Didier Galmiche ; Jean-Marc NotinSource :
English descriptors
Abstract
We propose a connection-based characterization of the multiplicative fragment of non-commutative logic (MNL), that is a conservative extension of both commutative (MLL) and non-commutative or cyclic (MCyLL) linear logic. It is based on a characterization for MLL together with the introduction of labels and constraints from a formula polarization process. We also study a similar characterization for the intuitionistic fragment of MNL. Finally, we consider the relationships between these results and proof nets construction in MNL based on labels and constraints.
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<profileDesc><textClass><keywords scheme="KwdEn" xml:lang="en"><term>connection method</term>
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<front><div type="abstract" xml:lang="en" wicri:score="3028">We propose a connection-based characterization of the multiplicative fragment of non-commutative logic (MNL), that is a conservative extension of both commutative (MLL) and non-commutative or cyclic (MCyLL) linear logic. It is based on a characterization for MLL together with the introduction of labels and constraints from a formula polarization process. We also study a similar characterization for the intuitionistic fragment of MNL. Finally, we consider the relationships between these results and proof nets construction in MNL based on labels and constraints.</div>
</front>
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<BibTex type="inproceedings"><ref>galmiche03b</ref>
<crinnumber>A03-R-210</crinnumber>
<category>3</category>
<equipe>TYPES</equipe>
<author><e>Galmiche, Didier</e>
<e>Notin, Jean-Marc</e>
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<title>Connection-based proof construction in Non-Commutative Logic</title>
<booktitle>{10th International Conference on Logic for Programming Artificial Intelligence and Reasoning 2003 - LPAR'03, Almaty, Kazakhstan}</booktitle>
<year>2003</year>
<volume>2850</volume>
<series>Lecture Notes in Computer Science</series>
<pages>422 - 436</pages>
<month>Sep</month>
<publisher>Springer Verlag</publisher>
<keywords><e>linear logic</e>
<e>non-commutative logic</e>
<e>connection method</e>
<e>labels</e>
<e>constraints</e>
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<abstract>We propose a connection-based characterization of the multiplicative fragment of non-commutative logic (MNL), that is a conservative extension of both commutative (MLL) and non-commutative or cyclic (MCyLL) linear logic. It is based on a characterization for MLL together with the introduction of labels and constraints from a formula polarization process. We also study a similar characterization for the intuitionistic fragment of MNL. Finally, we consider the relationships between these results and proof nets construction in MNL based on labels and constraints.</abstract>
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