On Proof Nets for Multiplicative Linear Logic with Units
Identifieur interne : 004D70 ( Hal/Checkpoint ); précédent : 004D69; suivant : 004D71On Proof Nets for Multiplicative Linear Logic with Units
Auteurs : Lutz Strassburger [France] ; François Lamarche [France]Source :
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Abstract
In this paper a theory of proof nets for multiplicative linear logic is presented, which includes the two multiplicative units. It naturally extends the well-known theory of unit-free multiplicative proof nets: A linking is no longer a set of axiom links but a tree in which the axiom links are subtrees. These trees will be identified according to an equivalence relation based on a simple form of graph rewriting. We will have the standard results of sequentialisation and strong normalisation of cut elimination. Furthermore, the identifications enforced on proofs are such that the proof nets, as they are presented here, form the arrows of the free (symmetric) *-autonomous category.
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xml:lang="en">In this paper a theory of proof nets for multiplicative linear logic is presented, which includes the two multiplicative units. It naturally extends the well-known theory of unit-free multiplicative proof nets: A linking is no longer a set of axiom links but a tree in which the axiom links are subtrees. These trees will be identified according to an equivalence relation based on a simple form of graph rewriting. We will have the standard results of sequentialisation and strong normalisation of cut elimination. Furthermore, the identifications enforced on proofs are such that the proof nets, as they are presented here, form the arrows of the free (symmetric) *-autonomous category.</div></front></TEI><hal api="V3"><titleStmt><title xml:lang="en">On Proof Nets for Multiplicative Linear Logic with Units</title><author role="aut"><persName><forename type="first">Lutz</forename><surname>Strassburger</surname></persName><email></email><idno type="halauthor">131128</idno><orgName ref="#struct-300009"></orgName><affiliation ref="#struct-2347"></affiliation></author><author role="aut"><persName><forename type="first">François</forename><surname>Lamarche</surname></persName><email></email><idno type="idhal">francois-lamarche</idno><idno type="halauthor">129932</idno><orgName ref="#struct-300009"></orgName><affiliation ref="#struct-2347"></affiliation></author><editor role="depositor"><persName><forename>Publications</forename><surname>Loria</surname></persName><email>publications@loria.fr</email></editor></titleStmt><editionStmt><edition n="v1" type="current"><date type="whenSubmitted">2006-09-26 10:16:04</date><date type="whenModified">2016-05-19 01:09:06</date><date type="whenReleased">2006-09-28 15:22:47</date><date type="whenProduced">2004</date></edition><respStmt><resp>contributor</resp><name key="108626"><persName><forename>Publications</forename><surname>Loria</surname></persName><email>publications@loria.fr</email></name></respStmt></editionStmt><publicationStmt><distributor>CCSD</distributor><idno type="halId">inria-00100244</idno><idno type="halUri">https://hal.inria.fr/inria-00100244</idno><idno type="halBibtex">strassburger:inria-00100244</idno><idno type="halRefHtml">Jerzy Marcinkowski and Andrzej Tarlecki. 18th International Workshop on Computer Science Logic - CSL'2004, 2004, Karpacz, Poland, Springer-Verlag, 3210, pp.145--159, 2004, Lecture Notes in Computer Science</idno><idno type="halRef">Jerzy Marcinkowski and Andrzej Tarlecki. 18th International Workshop on Computer Science Logic - CSL'2004, 2004, Karpacz, Poland, Springer-Verlag, 3210, pp.145--159, 2004, Lecture Notes in Computer Science</idno></publicationStmt><seriesStmt><idno type="stamp" n="INRIA">INRIA - Institut National de Recherche en Informatique et en Automatique</idno><idno type="stamp" n="CNRS">CNRS - Centre national de la recherche scientifique</idno><idno type="stamp" n="INPL">Institut National Polytechnique de Lorraine</idno><idno type="stamp" n="LORIA2">Publications du LORIA</idno><idno type="stamp" n="INRIA-NANCY-GRAND-EST">INRIA Nancy - Grand Est</idno><idno type="stamp" n="LORIA">LORIA - Laboratoire Lorrain de Recherche en Informatique et ses Applications</idno><idno type="stamp" n="LORIA-TALC" p="LORIA">Traitement automatique des langues et des connaissances</idno><idno type="stamp" n="UNIV-LORRAINE">Université de Lorraine</idno><idno type="stamp" n="INRIA-LORRAINE">INRIA Nancy - Grand Est</idno><idno type="stamp" n="LABO-LORIA-SET" p="LORIA">LABO-LORIA-SET</idno></seriesStmt><notesStmt><note type="commentary">13th Annual Conference of the EACSL. Colloque avec actes et comité de lecture. internationale.</note><note type="audience" n="2">International</note><note type="invited" n="0">No</note><note type="popular" n="0">No</note><note type="peer" n="1">Yes</note><note type="proceedings" n="1">Yes</note></notesStmt><sourceDesc><biblStruct><analytic><title xml:lang="en">On Proof Nets for Multiplicative Linear Logic with Units</title><author role="aut"><persName><forename type="first">Lutz</forename><surname>Strassburger</surname></persName><idno type="halAuthorId">131128</idno><orgName ref="#struct-300009"></orgName><affiliation ref="#struct-2347"></affiliation></author><author role="aut"><persName><forename type="first">François</forename><surname>Lamarche</surname></persName><idno type="idHal">francois-lamarche</idno><idno type="halAuthorId">129932</idno><orgName ref="#struct-300009"></orgName><affiliation ref="#struct-2347"></affiliation></author></analytic><monogr><idno type="localRef">A04-R-032 || strassburger04a</idno><meeting><title>18th International Workshop on Computer Science Logic - CSL'2004</title><date type="start">2004</date><settlement>Karpacz, Poland</settlement></meeting><editor>Jerzy Marcinkowski and Andrzej Tarlecki</editor><imprint><publisher>Springer-Verlag</publisher><biblScope unit="serie">Lecture Notes in Computer Science</biblScope><biblScope unit="volume">3210</biblScope><biblScope unit="pp">145--159</biblScope><date type="datePub">2004</date></imprint></monogr></biblStruct></sourceDesc><profileDesc><langUsage><language ident="en">English</language></langUsage><textClass><keywords scheme="author"><term xml:lang="fr">logique linéaire</term><term xml:lang="fr">autonomy</term><term xml:lang="fr">linear logic</term><term xml:lang="fr">proof nets</term><term xml:lang="fr">cut elimination</term><term xml:lang="fr">réseaux de démonstration</term><term xml:lang="fr">élimination de coupures</term><term xml:lang="fr">autonomie</term></keywords><classCode scheme="halDomain" n="info.info-oh">Computer Science [cs]/Other [cs.OH]</classCode><classCode scheme="halTypology" n="COMM">Conference papers</classCode></textClass><abstract xml:lang="en">In this paper a theory of proof nets for multiplicative linear logic is presented, which includes the two multiplicative units. It naturally extends the well-known theory of unit-free multiplicative proof nets: A linking is no longer a set of axiom links but a tree in which the axiom links are subtrees. These trees will be identified according to an equivalence relation based on a simple form of graph rewriting. We will have the standard results of sequentialisation and strong normalisation of cut elimination. Furthermore, the identifications enforced on proofs are such that the proof nets, as they are presented here, form the arrows of the free (symmetric) *-autonomous category.</abstract></profileDesc></hal></record>Pour manipuler ce document sous Unix (Dilib)
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