A Connection-Based Characterization of Bi-intuitionistic Validity
Identifieur interne : 003470 ( Istex/Corpus ); précédent : 003469; suivant : 003471A Connection-Based Characterization of Bi-intuitionistic Validity
Auteurs : Didier Galmiche ; Daniel MérySource :
- Lecture Notes in Computer Science [ 0302-9743 ]
Abstract
Abstract: We give a connection-based characterization of validity in propositional bi-intuitionistic logic in terms of specific directed graphs called R-graphs. Such a characterization is well-suited for deriving labelled proof-systems with counter-model construction facilities. We first define the notion of bi-intuitionistic R-graph from which we then obtain a connection-based characterization of propositional bi-intuitionistic validity and derive a sound and complete free-variable labelled sequent calculus that admits cut-elimination and also variable splitting.
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DOI: 10.1007/978-3-642-22438-6_21
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TocLevels="0"><BookID>978-3-642-22438-6</BookID><BookTitle>Automated Deduction – CADE-23</BookTitle><BookSubTitle>23rd International Conference on Automated Deduction, Wrocław, Poland, July 31 - August 5, 2011. Proceedings</BookSubTitle><BookVolumeNumber>6803</BookVolumeNumber><BookSequenceNumber>6803</BookSequenceNumber><BookDOI>10.1007/978-3-642-22438-6</BookDOI><BookTitleID>271766</BookTitleID><BookPrintISBN>978-3-642-22437-9</BookPrintISBN><BookElectronicISBN>978-3-642-22438-6</BookElectronicISBN><BookChapterCount>38</BookChapterCount><BookCopyright><CopyrightHolderName>Springer-Verlag GmbH Berlin Heidelberg</CopyrightHolderName><CopyrightYear>2011</CopyrightYear></BookCopyright><BookSubjectGroup><BookSubject Code="I" Type="Primary">Computer Science</BookSubject><BookSubject Code="I21017" Priority="1" Type="Secondary">Artificial Intelligence (incl. Robotics)</BookSubject><BookSubject Code="I16048" Priority="2" Type="Secondary">Mathematical Logic and Formal Languages</BookSubject><BookSubject Code="I1603X" Priority="3" Type="Secondary">Logics and Meanings of Programs</BookSubject><BookSubject Code="I14029" Priority="4" Type="Secondary">Software Engineering</BookSubject><SubjectCollection Code="SUCO11645">Computer Science</SubjectCollection></BookSubjectGroup><BookContext><SeriesID>558</SeriesID><SubSeriesID>1244</SubSeriesID></BookContext></BookInfo><BookHeader><EditorGroup><Editor AffiliationIDS="Aff19"><EditorName DisplayOrder="Western"><GivenName>Nikolaj</GivenName><FamilyName>Bjørner</FamilyName></EditorName><Contact><Email>nbjorner@microsoft.com</Email></Contact></Editor><Editor AffiliationIDS="Aff20"><EditorName DisplayOrder="Western"><GivenName>Viorica</GivenName><FamilyName>Sofronie-Stokkermans</FamilyName></EditorName><Contact><Email>sofronie@mpi-inf.mpg.de</Email></Contact></Editor><Affiliation ID="Aff19"><OrgName>Microsoft Research</OrgName><OrgAddress><Street>One Microsoft Way</Street><Postcode>98052-6399</Postcode><City>Redmond</City><State>WA</State><Country>USA</Country></OrgAddress></Affiliation><Affiliation ID="Aff20"><OrgName>Max-Planck-Institut für Informatik</OrgName><OrgAddress><Street>Campus E 1.4</Street><Postcode>66123</Postcode><City>Saarbrücken</City><Country>Germany</Country></OrgAddress></Affiliation></EditorGroup></BookHeader><Chapter ID="Chap21" Language="En"><ChapterInfo ChapterType="OriginalPaper" ContainsESM="No" NumberingDepth="2" NumberingStyle="ContentOnly" TocLevels="0"><ChapterID>21</ChapterID><ChapterDOI>10.1007/978-3-642-22438-6_21</ChapterDOI><ChapterSequenceNumber>21</ChapterSequenceNumber><ChapterTitle Language="En">A Connection-Based Characterization of Bi-intuitionistic Validity</ChapterTitle><ChapterFirstPage>268</ChapterFirstPage><ChapterLastPage>282</ChapterLastPage><ChapterCopyright><CopyrightHolderName>Springer-Verlag Berlin Heidelberg</CopyrightHolderName><CopyrightYear>2011</CopyrightYear></ChapterCopyright><ChapterGrants Type="Regular"><MetadataGrant Grant="OpenAccess"></MetadataGrant><AbstractGrant Grant="OpenAccess"></AbstractGrant><BodyPDFGrant Grant="Restricted"></BodyPDFGrant><BodyHTMLGrant Grant="Restricted"></BodyHTMLGrant><BibliographyGrant Grant="Restricted"></BibliographyGrant><ESMGrant Grant="Restricted"></ESMGrant></ChapterGrants><ChapterContext><SeriesID>558</SeriesID><BookID>978-3-642-22438-6</BookID><BookTitle>Automated Deduction – CADE-23</BookTitle></ChapterContext></ChapterInfo><ChapterHeader><AuthorGroup><Author AffiliationIDS="Aff21"><AuthorName DisplayOrder="Western"><GivenName>Didier</GivenName><FamilyName>Galmiche</FamilyName></AuthorName></Author><Author AffiliationIDS="Aff21"><AuthorName DisplayOrder="Western"><GivenName>Daniel</GivenName><FamilyName>Méry</FamilyName></AuthorName></Author><Affiliation ID="Aff21"><OrgName>LORIA - Université Henri Poincaré</OrgName><OrgAddress><Street>Campus Scientifique</Street><Postbox>BP 239</Postbox><City>Vandœuvre-lés-Nancy</City><Country>France</Country></OrgAddress></Affiliation></AuthorGroup><Abstract ID="Abs1" Language="En"><Heading>Abstract</Heading><Para>We give a connection-based characterization of validity in propositional bi-intuitionistic logic in terms of specific directed graphs called R-graphs. Such a characterization is well-suited for deriving labelled proof-systems with counter-model construction facilities. We first define the notion of bi-intuitionistic R-graph from which we then obtain a connection-based characterization of propositional bi-intuitionistic validity and derive a sound and complete free-variable labelled sequent calculus that admits cut-elimination and also variable splitting.</Para></Abstract></ChapterHeader><NoBody></NoBody></Chapter></Book></Series></Publisher></istex:document></istex:metadataXml><mods version="3.6"><titleInfo lang="en"><title>A Connection-Based Characterization of Bi-intuitionistic Validity</title></titleInfo><titleInfo type="alternative" contentType="CDATA"><title>A Connection-Based Characterization of Bi-intuitionistic Validity</title></titleInfo><name type="personal"><namePart type="given">Didier</namePart><namePart type="family">Galmiche</namePart><affiliation>LORIA - Université Henri Poincaré, Campus Scientifique, BP 239, Vandœuvre-lés-Nancy, France</affiliation><role><roleTerm type="text">author</roleTerm></role></name><name type="personal"><namePart type="given">Daniel</namePart><namePart type="family">Méry</namePart><affiliation>LORIA - Université Henri Poincaré, Campus Scientifique, BP 239, Vandœuvre-lés-Nancy, France</affiliation><role><roleTerm type="text">author</roleTerm></role></name><typeOfResource>text</typeOfResource><genre displayLabel="OriginalPaper" authority="ISTEX" authorityURI="https://content-type.data.istex.fr" type="conference" valueURI="https://content-type.data.istex.fr/ark:/67375/XTP-BFHXPBJJ-3">conference</genre><originInfo><publisher>Springer Berlin Heidelberg</publisher><place><placeTerm type="text">Berlin, Heidelberg</placeTerm></place><dateIssued encoding="w3cdtf">2011</dateIssued><copyrightDate encoding="w3cdtf">2011</copyrightDate></originInfo><language><languageTerm type="code" authority="rfc3066">en</languageTerm><languageTerm type="code" authority="iso639-2b">eng</languageTerm></language><abstract lang="en">Abstract: We give a connection-based characterization of validity in propositional bi-intuitionistic logic in terms of specific directed graphs called R-graphs. Such a characterization is well-suited for deriving labelled proof-systems with counter-model construction facilities. We first define the notion of bi-intuitionistic R-graph from which we then obtain a connection-based characterization of propositional bi-intuitionistic validity and derive a sound and complete free-variable labelled sequent calculus that admits cut-elimination and also variable splitting.</abstract><relatedItem type="host"><titleInfo><title>Automated Deduction – CADE-23</title><subTitle>23rd International Conference on Automated Deduction, Wrocław, Poland, July 31 - August 5, 2011. Proceedings</subTitle></titleInfo><name type="personal"><namePart type="given">Nikolaj</namePart><namePart type="family">Bjørner</namePart><affiliation>Microsoft Research, One Microsoft Way, 98052-6399, Redmond, WA, USA</affiliation><affiliation>E-mail: nbjorner@microsoft.com</affiliation><role><roleTerm type="text">editor</roleTerm></role></name><name type="personal"><namePart type="given">Viorica</namePart><namePart type="family">Sofronie-Stokkermans</namePart><affiliation>Max-Planck-Institut für Informatik, Campus E 1.4, 66123, Saarbrücken, Germany</affiliation><affiliation>E-mail: sofronie@mpi-inf.mpg.de</affiliation><role><roleTerm type="text">editor</roleTerm></role></name><genre type="book-series" authority="ISTEX" authorityURI="https://publication-type.data.istex.fr" valueURI="https://publication-type.data.istex.fr/ark:/67375/JMC-0G6R5W5T-Z">book-series</genre><originInfo><publisher>Springer</publisher><copyrightDate encoding="w3cdtf">2011</copyrightDate><issuance>monographic</issuance></originInfo><subject><genre>Book-Subject-Collection</genre><topic authority="SpringerSubjectCodes" authorityURI="SUCO11645">Computer Science</topic></subject><subject><genre>Book-Subject-Group</genre><topic authority="SpringerSubjectCodes" authorityURI="I">Computer Science</topic><topic authority="SpringerSubjectCodes" authorityURI="I21017">Artificial Intelligence (incl. Robotics)</topic><topic authority="SpringerSubjectCodes" authorityURI="I16048">Mathematical Logic and Formal Languages</topic><topic authority="SpringerSubjectCodes" authorityURI="I1603X">Logics and Meanings of Programs</topic><topic authority="SpringerSubjectCodes" authorityURI="I14029">Software Engineering</topic></subject><identifier type="DOI">10.1007/978-3-642-22438-6</identifier><identifier type="ISBN">978-3-642-22437-9</identifier><identifier type="eISBN">978-3-642-22438-6</identifier><identifier type="ISSN">0302-9743</identifier><identifier type="eISSN">1611-3349</identifier><identifier type="BookTitleID">271766</identifier><identifier type="BookID">978-3-642-22438-6</identifier><identifier type="BookChapterCount">38</identifier><identifier type="BookVolumeNumber">6803</identifier><identifier type="BookSequenceNumber">6803</identifier><part><date>2011</date><detail type="volume"><number>6803</number><caption>vol.</caption></detail><extent 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type="given">Jon</namePart><namePart type="given">M.</namePart><namePart type="family">Kleinberg</namePart><affiliation>Cornell University, Ithaca, NY, USA</affiliation><role><roleTerm type="text">editor</roleTerm></role></name><name type="personal"><namePart type="given">Friedemann</namePart><namePart type="family">Mattern</namePart><affiliation>ETH Zurich, Zurich, Switzerland</affiliation><role><roleTerm type="text">editor</roleTerm></role></name><name type="personal"><namePart type="given">John</namePart><namePart type="given">C.</namePart><namePart type="family">Mitchell</namePart><affiliation>Stanford University, Stanford, CA, USA</affiliation><role><roleTerm type="text">editor</roleTerm></role></name><name type="personal"><namePart type="given">Moni</namePart><namePart type="family">Naor</namePart><affiliation>Weizmann Institute of Science, Rehovot, Israel</affiliation><role><roleTerm type="text">editor</roleTerm></role></name><name type="personal"><namePart type="given">Oscar</namePart><namePart type="family">Nierstrasz</namePart><affiliation>University of Bern, Bern, Switzerland</affiliation><role><roleTerm type="text">editor</roleTerm></role></name><name type="personal"><namePart type="given">C.</namePart><namePart type="family">Pandu Rangan</namePart><affiliation>Indian Institute of Technology, Madras, India</affiliation><role><roleTerm type="text">editor</roleTerm></role></name><name type="personal"><namePart type="given">Bernhard</namePart><namePart type="family">Steffen</namePart><affiliation>University of Dortmund, Dortmund, Germany</affiliation><role><roleTerm type="text">editor</roleTerm></role></name><name type="personal"><namePart type="given">Madhu</namePart><namePart type="family">Sudan</namePart><affiliation>Massachusetts Institute of Technology, MA, USA</affiliation><role><roleTerm type="text">editor</roleTerm></role></name><name type="personal"><namePart type="given">Demetri</namePart><namePart type="family">Terzopoulos</namePart><affiliation>University of California, Los Angeles, CA, USA</affiliation><role><roleTerm type="text">editor</roleTerm></role></name><name type="personal"><namePart type="given">Doug</namePart><namePart type="family">Tygar</namePart><affiliation>University of California, Berkeley, CA, USA</affiliation><role><roleTerm type="text">editor</roleTerm></role></name><name type="personal"><namePart type="given">Moshe</namePart><namePart type="given">Y.</namePart><namePart type="family">Vardi</namePart><affiliation>Rice University, Houston, TX, USA</affiliation><role><roleTerm type="text">editor</roleTerm></role></name><name type="personal"><namePart type="given">Gerhard</namePart><namePart type="family">Weikum</namePart><affiliation>Max-Planck Institute of Computer Science, Saarbrücken, Germany</affiliation><role><roleTerm type="text">editor</roleTerm></role></name><originInfo><publisher>Springer</publisher><copyrightDate encoding="w3cdtf">2011</copyrightDate><issuance>serial</issuance></originInfo><relatedItem type="constituent"><titleInfo><title>Lecture Notes in Artificial Intelligence</title></titleInfo><name type="personal"><namePart type="given">David</namePart><namePart type="family">Hutchison</namePart><affiliation>Lancaster University, Lancaster, UK</affiliation><role><roleTerm type="text">editor</roleTerm></role></name><name type="personal"><namePart type="given">Takeo</namePart><namePart type="family">Kanade</namePart><affiliation>Carnegie Mellon University, Pittsburgh, PA, USA</affiliation><role><roleTerm type="text">editor</roleTerm></role></name><name type="personal"><namePart type="given">Josef</namePart><namePart type="family">Kittler</namePart><affiliation>University of Surrey, Guildford, UK</affiliation><role><roleTerm type="text">editor</roleTerm></role></name><name type="personal"><namePart type="given">Jon</namePart><namePart type="given">M.</namePart><namePart type="family">Kleinberg</namePart><affiliation>Cornell University, Ithaca, NY, USA</affiliation><role><roleTerm type="text">editor</roleTerm></role></name><name type="personal"><namePart type="given">Friedemann</namePart><namePart type="family">Mattern</namePart><affiliation>ETH Zurich, Zurich, Switzerland</affiliation><role><roleTerm type="text">editor</roleTerm></role></name><name type="personal"><namePart type="given">John</namePart><namePart type="given">C.</namePart><namePart type="family">Mitchell</namePart><affiliation>Stanford University, Stanford, CA, USA</affiliation><role><roleTerm type="text">editor</roleTerm></role></name><name type="personal"><namePart type="given">Moni</namePart><namePart type="family">Naor</namePart><affiliation>Weizmann Institute of Science, Rehovot, Israel</affiliation><role><roleTerm type="text">editor</roleTerm></role></name><name type="personal"><namePart type="given">Oscar</namePart><namePart type="family">Nierstrasz</namePart><affiliation>University of Bern, Bern, Switzerland</affiliation><role><roleTerm type="text">editor</roleTerm></role></name><name type="personal"><namePart type="given">C.</namePart><namePart type="family">Pandu Rangan</namePart><affiliation>Indian Institute of Technology, Madras, India</affiliation><role><roleTerm type="text">editor</roleTerm></role></name><name type="personal"><namePart type="given">Bernhard</namePart><namePart type="family">Steffen</namePart><affiliation>University of Dortmund, Dortmund, Germany</affiliation><role><roleTerm type="text">editor</roleTerm></role></name><name type="personal"><namePart type="given">Madhu</namePart><namePart type="family">Sudan</namePart><affiliation>Massachusetts Institute of Technology, MA, USA</affiliation><role><roleTerm type="text">editor</roleTerm></role></name><name type="personal"><namePart type="given">Demetri</namePart><namePart type="family">Terzopoulos</namePart><affiliation>University of 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