On Proof Nets for Multiplicative Linear Logic with Units
Identifieur interne : 006F41 ( Main/Exploration ); précédent : 006F40; suivant : 006F42On Proof Nets for Multiplicative Linear Logic with Units
Auteurs : Lutz Strassburger [France] ; François Lamarche [France]Source :
Descripteurs français
- mix :
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.
Url:
Affiliations:
- France
- Grand Est, Lorraine (région)
- Nancy
- Institut national polytechnique de Lorraine, Université Nancy 2, Université de Lorraine
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Le document en format XML
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<front><div type="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.</div>
</front>
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<affiliations><list><country><li>France</li>
</country>
<region><li>Grand Est</li>
<li>Lorraine (région)</li>
</region>
<settlement><li>Nancy</li>
</settlement>
<orgName><li>Institut national polytechnique de Lorraine</li>
<li>Université Nancy 2</li>
<li>Université de Lorraine</li>
</orgName>
</list>
<tree><country name="France"><region name="Grand Est"><name sortKey="Strassburger, Lutz" sort="Strassburger, Lutz" uniqKey="Strassburger L" first="Lutz" last="Strassburger">Lutz Strassburger</name>
</region>
<name sortKey="Lamarche, Francois" sort="Lamarche, Francois" uniqKey="Lamarche F" first="François" last="Lamarche">François Lamarche</name>
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