Naming Proofs in Classical Propositional Logic
Identifieur interne : 006226 ( Main/Exploration ); précédent : 006225; suivant : 006227Naming Proofs in Classical Propositional Logic
Auteurs : François Lamarche [France] ; Lutz Stra Burger [Allemagne]Source :
- Lecture Notes in Computer Science [ 0302-9743 ]
Descripteurs français
- Pascal (Inist)
English descriptors
- KwdEn :
Abstract
Abstract: We present a theory of proof denotations in classical propositional logic. The abstract definition is in terms of a semiring of weights, and two concrete instances are explored. With the Boolean semiring we get a theory of classical proof nets, with a geometric correctness criterion, a sequentialization theorem, and a strongly normalizing cut-elimination procedure. This gives us a “Boolean” category, which is not a poset. With the semiring of natural numbers, we obtain a sound semantics for classical logic, in which fewer proofs are identified. Though a “real” sequentialization theorem is missing, these proof nets have a grip on complexity issues. In both cases the cut elimination procedure is closely related to its equivalent in the calculus of structures.
Url:
DOI: 10.1007/11417170_19
Affiliations:
Links toward previous steps (curation, corpus...)
- to stream Istex, to step Corpus: 002559
- to stream Istex, to step Curation: 002528
- to stream Istex, to step Checkpoint: 001540
- to stream Main, to step Merge: 006451
- to stream PascalFrancis, to step Corpus: 000535
- to stream PascalFrancis, to step Curation: 000503
- to stream PascalFrancis, to step Checkpoint: 000476
- to stream Main, to step Merge: 006613
- to stream Main, to step Curation: 006226
Le document en format XML
<record><TEI wicri:istexFullTextTei="biblStruct"><teiHeader><fileDesc><titleStmt><title xml:lang="en">Naming Proofs in Classical Propositional Logic</title><author><name sortKey="Lamarche, Francois" sort="Lamarche, Francois" uniqKey="Lamarche F" first="François" last="Lamarche">François Lamarche</name></author><author><name sortKey="Stra Burger, Lutz" sort="Stra Burger, Lutz" uniqKey="Stra Burger L" first="Lutz" last="Stra Burger">Lutz Stra Burger</name></author></titleStmt><publicationStmt><idno type="wicri:source">ISTEX</idno><idno type="RBID">ISTEX:9FF4C3F07DCCE03EF61160B08D101D9539DAC17D</idno><date when="2005" year="2005">2005</date><idno type="doi">10.1007/11417170_19</idno><idno type="url">https://api.istex.fr/ark:/67375/HCB-81297222-2/fulltext.pdf</idno><idno type="wicri:Area/Istex/Corpus">002559</idno><idno type="wicri:explorRef" wicri:stream="Istex" wicri:step="Corpus" wicri:corpus="ISTEX">002559</idno><idno type="wicri:Area/Istex/Curation">002528</idno><idno type="wicri:Area/Istex/Checkpoint">001540</idno><idno type="wicri:explorRef" wicri:stream="Istex" wicri:step="Checkpoint">001540</idno><idno type="wicri:doubleKey">0302-9743:2005:Lamarche F:naming:proofs:in</idno><idno type="wicri:Area/Main/Merge">006451</idno><idno type="wicri:source">INIST</idno><idno type="RBID">Pascal:05-0358285</idno><idno type="wicri:Area/PascalFrancis/Corpus">000535</idno><idno type="wicri:Area/PascalFrancis/Curation">000503</idno><idno type="wicri:Area/PascalFrancis/Checkpoint">000476</idno><idno type="wicri:explorRef" wicri:stream="PascalFrancis" wicri:step="Checkpoint">000476</idno><idno type="wicri:doubleKey">0302-9743:2005:Lamarche F:naming:proofs:in</idno><idno type="wicri:Area/Main/Merge">006613</idno><idno type="wicri:Area/Main/Curation">006226</idno><idno type="wicri:Area/Main/Exploration">006226</idno></publicationStmt><sourceDesc><biblStruct><analytic><title level="a" type="main" xml:lang="en">Naming Proofs in Classical Propositional Logic</title><author><name sortKey="Lamarche, Francois" sort="Lamarche, Francois" uniqKey="Lamarche F" first="François" last="Lamarche">François Lamarche</name><affiliation wicri:level="3"><country xml:lang="fr">France</country><wicri:regionArea>LORIA & INRIA-Lorraine, Projet Calligramme, 615, rue du Jardin Botanique, 54602, Villers-lès-Nancy</wicri:regionArea><placeName><region type="region" nuts="2">Grand Est</region><region type="old region" nuts="2">Lorraine (région)</region><settlement type="city">Villers-lès-Nancy</settlement></placeName></affiliation></author><author><name sortKey="Stra Burger, Lutz" sort="Stra Burger, Lutz" uniqKey="Stra Burger L" first="Lutz" last="Stra Burger">Lutz Stra Burger</name><affiliation wicri:level="3"><country xml:lang="fr">Allemagne</country><wicri:regionArea>Informatik — Programmiersysteme, Universität des Saarlandes, Postfach 15 11 50, 66041, Saarbrücken</wicri:regionArea><placeName><region type="land" nuts="2">Sarre (Land)</region><settlement type="city">Sarrebruck</settlement></placeName></affiliation></author></analytic><monogr></monogr><series><title level="s" type="main" xml:lang="en">Lecture Notes in Computer Science</title><idno type="ISSN">0302-9743</idno><idno type="eISSN">1611-3349</idno><idno type="ISSN">0302-9743</idno></series></biblStruct></sourceDesc><seriesStmt><idno type="ISSN">0302-9743</idno></seriesStmt></fileDesc><profileDesc><textClass><keywords scheme="KwdEn" xml:lang="en"><term>Boolean logic</term><term>Cut elimination</term><term>Distributed system</term><term>First order logic</term><term>Lambda calculus</term><term>Naming</term><term>Partial ordering</term><term>Proof net</term><term>Proof theory</term><term>Propositional logic</term><term>Semantics</term><term>Semiring</term><term>Type theory</term></keywords><keywords scheme="Pascal" xml:lang="fr"><term>.</term><term>Dénomination</term><term>Elimination coupure</term><term>Lambda calcul</term><term>Logique booléenne</term><term>Logique ordre 1</term><term>Logique propositionnelle</term><term>Relation ordre partiel</term><term>Réseau preuve</term><term>Semianneau</term><term>Système réparti</term><term>Sémantique</term><term>Théorie preuve</term><term>Théorie type</term></keywords></textClass></profileDesc></teiHeader><front><div type="abstract" xml:lang="en">Abstract: We present a theory of proof denotations in classical propositional logic. The abstract definition is in terms of a semiring of weights, and two concrete instances are explored. With the Boolean semiring we get a theory of classical proof nets, with a geometric correctness criterion, a sequentialization theorem, and a strongly normalizing cut-elimination procedure. This gives us a “Boolean” category, which is not a poset. With the semiring of natural numbers, we obtain a sound semantics for classical logic, in which fewer proofs are identified. Though a “real” sequentialization theorem is missing, these proof nets have a grip on complexity issues. In both cases the cut elimination procedure is closely related to its equivalent in the calculus of structures.</div></front></TEI><affiliations><list><country><li>Allemagne</li><li>France</li></country><region><li>Grand Est</li><li>Lorraine (région)</li><li>Sarre (Land)</li></region><settlement><li>Sarrebruck</li><li>Villers-lès-Nancy</li></settlement></list><tree><country name="France"><region name="Grand Est"><name sortKey="Lamarche, Francois" sort="Lamarche, Francois" uniqKey="Lamarche F" first="François" last="Lamarche">François Lamarche</name></region></country><country name="Allemagne"><region name="Sarre (Land)"><name sortKey="Stra Burger, Lutz" sort="Stra Burger, Lutz" uniqKey="Stra Burger L" first="Lutz" last="Stra Burger">Lutz Stra Burger</name></region></country></tree></affiliations></record>Pour manipuler ce document sous Unix (Dilib)
EXPLOR_STEP=$WICRI_ROOT/Wicri/Lorraine/explor/InforLorV4/Data/Main/Exploration
HfdSelect -h $EXPLOR_STEP/biblio.hfd -nk 006226 | SxmlIndent | more
Ou
HfdSelect -h $EXPLOR_AREA/Data/Main/Exploration/biblio.hfd -nk 006226 | SxmlIndent | more
Pour mettre un lien sur cette page dans le réseau Wicri
{{Explor lien
|wiki= Wicri/Lorraine
|area= InforLorV4
|flux= Main
|étape= Exploration
|type= RBID
|clé= ISTEX:9FF4C3F07DCCE03EF61160B08D101D9539DAC17D
|texte= Naming Proofs in Classical Propositional Logic
}}
| This area was generated with Dilib version V0.6.33. |  |