A Modal BI Logic for Dynamic Resource Properties
Identifieur interne : 000D86 ( Istex/Corpus ); précédent : 000D85; suivant : 000D87A Modal BI Logic for Dynamic Resource Properties
Auteurs : J. R. Courtault ; D. GalmicheSource :
- Lecture Notes in Computer Science [ 0302-9743 ]
Abstract
Abstract: The logic of Bunched implications (BI) and its variants or extensions provide a powerful framework to deal with resources having static properties. In this paper, we propose a modal extension of BI logic, called DBI, which allows us to deal with dynamic resource properties. After defining a Kripke semantics for DBI, we illustrate the interest of DBI for expressing some dynamic properties and then we propose a labelled tableaux calculus for this logic. This calculus is proved sound and complete w.r.t. the Kripke semantics. Moreover, we also give a method for countermodel generation in this logic.
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DOI: 10.1007/978-3-642-35722-0_10
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After defining a Kripke semantics for DBI, we illustrate the interest of DBI for expressing some dynamic properties and then we propose a labelled tableaux calculus for this logic. This calculus is proved sound and complete w.r.t. the Kripke semantics. Moreover, we also give a method for countermodel generation in this logic.</div></front></TEI><istex><corpusName>springer-ebooks</corpusName><author><json:item><name>J. R. Courtault</name><affiliations><json:string>Université de Lorraine – LORIA UMR 7503, Campus Scientifique, BP 239, Vandœuvre-lès-Nancy, France</json:string></affiliations></json:item><json:item><name>D. 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University</orgName><address><settlement>Houston</settlement><region>TX</region><country key="US">UNITED STATES</country></address></affiliation></editor><editor><persName><forename type="first">Gerhard</forename><surname>Weikum</surname></persName><affiliation><idno type="GRID" subtype="Institution">grid.419607.d</idno><idno type="ISNI" subtype="Institution">0000000120969941</idno><orgName type="institution">Max-Planck Institute of Computer Science</orgName><address><settlement>Saarbrücken</settlement><country key="DE">GERMANY</country></address></affiliation></editor><idno type="pISSN">0302-9743</idno><idno type="eISSN">1611-3349</idno><idno type="seriesID">558</idno></series></biblStruct></sourceDesc></fileDesc><profileDesc><abstract xml:lang="en"><head>Abstract</head><p>The logic of Bunched implications (BI) and its variants or extensions provide a powerful framework to deal with resources having static properties. In this paper, we propose a modal extension of BI logic, called DBI, which allows us to deal with dynamic resource properties. After defining a Kripke semantics for DBI, we illustrate the interest of DBI for expressing some dynamic properties and then we propose a labelled tableaux calculus for this logic. This calculus is proved sound and complete w.r.t. the Kripke semantics. 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Type="GRID">grid.5734.5</OrgID><OrgID Level="Institution" Type="ISNI">0000000107265157</OrgID><OrgName>University of Bern</OrgName><OrgAddress><City>Bern</City><Country>Switzerland</Country></OrgAddress></Affiliation><Affiliation ID="Aff9"><OrgID Level="Institution" Type="GRID">grid.417969.4</OrgID><OrgID Level="Institution" Type="ISNI">0000000123151926</OrgID><OrgName>Indian Institute of Technology</OrgName><OrgAddress><City>Madras</City><Country>India</Country></OrgAddress></Affiliation><Affiliation ID="Aff10"><OrgID Level="Institution" Type="GRID">grid.5675.1</OrgID><OrgID Level="Institution" Type="ISNI">0000000104169637</OrgID><OrgName>University of Dortmund</OrgName><OrgAddress><City>Dortmund</City><Country>Germany</Country></OrgAddress></Affiliation><Affiliation ID="Aff11"><OrgID Level="Institution" Type="GRID">grid.116068.8</OrgID><OrgID Level="Institution" Type="ISNI">0000000123412786</OrgID><OrgName>Massachusetts Institute of Technology</OrgName><OrgAddress><State>MA</State><Country>USA</Country></OrgAddress></Affiliation><Affiliation ID="Aff12"><OrgID Level="Institution" Type="GRID">grid.19006.3e</OrgID><OrgID Level="Institution" Type="ISNI">0000000096326718</OrgID><OrgName>University of California</OrgName><OrgAddress><City>Los Angeles</City><State>CA</State><Country>USA</Country></OrgAddress></Affiliation><Affiliation ID="Aff13"><OrgID Level="Institution" Type="GRID">grid.47840.3f</OrgID><OrgID Level="Institution" Type="ISNI">0000000121817878</OrgID><OrgName>University of California</OrgName><OrgAddress><City>Berkeley</City><State>CA</State><Country>USA</Country></OrgAddress></Affiliation><Affiliation ID="Aff14"><OrgID Level="Institution" Type="GRID">grid.21940.3e</OrgID><OrgID Level="Institution" Type="ISNI"> 0000000419368278</OrgID><OrgName>Rice University</OrgName><OrgAddress><City>Houston</City><State>TX</State><Country>USA</Country></OrgAddress></Affiliation><Affiliation ID="Aff15"><OrgID Level="Institution" Type="GRID">grid.419607.d</OrgID><OrgID Level="Institution" Type="ISNI">0000000120969941</OrgID><OrgName>Max-Planck Institute of Computer Science</OrgName><OrgAddress><City>Saarbrücken</City><Country>Germany</Country></OrgAddress></Affiliation></EditorGroup></SeriesHeader><Book Language="En"><BookInfo BookProductType="Proceedings" ContainsESM="No" Language="En" MediaType="eBook" NumberingDepth="2" NumberingStyle="ContentOnly" OutputMedium="All" TocLevels="0"><BookID>978-3-642-35722-0</BookID><BookTitle>Logical Foundations of Computer Science</BookTitle><BookSubTitle>International Symposium, LFCS 2013, San Diego, CA, USA, January 6-8, 2013. Proceedings</BookSubTitle><BookVolumeNumber>7734</BookVolumeNumber><BookSequenceNumber>7734</BookSequenceNumber><BookDOI>10.1007/978-3-642-35722-0</BookDOI><BookTitleID>311175</BookTitleID><BookPrintISBN>978-3-642-35721-3</BookPrintISBN><BookElectronicISBN>978-3-642-35722-0</BookElectronicISBN><BookChapterCount>29</BookChapterCount><BookCopyright><CopyrightHolderName>Springer-Verlag Berlin Heidelberg</CopyrightHolderName><CopyrightYear>2013</CopyrightYear></BookCopyright><BookSubjectGroup><BookSubject Code="SCI" Type="Primary">Computer Science</BookSubject><BookSubject Code="SCI16048" Priority="1" Type="Secondary">Mathematical Logic and Formal Languages</BookSubject><BookSubject Code="SCI12026" Priority="2" Type="Secondary">Arithmetic and Logic Structures</BookSubject><BookSubject Code="SCI1603X" Priority="3" Type="Secondary">Logics and Meanings of Programs</BookSubject><BookSubject Code="SCI16005" Priority="4" Type="Secondary">Theory of Computation</BookSubject><BookSubject Code="SCI14037" Priority="5" Type="Secondary">Programming Languages, Compilers, Interpreters</BookSubject><BookSubject Code="SCM24005" Priority="6" Type="Secondary">Mathematical Logic and Foundations</BookSubject><SubjectCollection Code="SUCO11645">Computer Science</SubjectCollection></BookSubjectGroup><BookContext><SeriesID>558</SeriesID></BookContext><ConferenceInfo><ConfSeriesName>International Symposium on Logical Foundations of Computer Science</ConfSeriesName><ConfSeriesID Type="Springer">lfcs</ConfSeriesID><ConfSeriesID Type="DBLP">lfcs</ConfSeriesID><ConfEventID Type="Springer">lfcs2013</ConfEventID><ConfEventAbbreviation>LFCS</ConfEventAbbreviation><ConfEventLocation><City>San Diego, CA</City><Country>USA</Country></ConfEventLocation><ConfEventDateStart><Year>2013</Year><Month>1</Month><Day>6</Day></ConfEventDateStart><ConfEventDateEnd><Year>2013</Year><Month>1</Month><Day>8</Day></ConfEventDateEnd></ConferenceInfo></BookInfo><BookHeader><EditorGroup><Editor AffiliationIDS="Aff16"><EditorName DisplayOrder="Western"><GivenName>Sergei</GivenName><FamilyName>Artemov</FamilyName></EditorName><Contact><Email>sartemov@gc.cuny.edu</Email></Contact></Editor><Editor AffiliationIDS="Aff17"><EditorName DisplayOrder="Western"><GivenName>Anil</GivenName><FamilyName>Nerode</FamilyName></EditorName><Contact><Email>anil@math.cornell.edu</Email></Contact></Editor><Affiliation ID="Aff16"><OrgID Level="Institution" Type="GRID">grid.253482.a</OrgID><OrgID Level="Institution" Type="ISNI">0000000101707903</OrgID><OrgDivision>Computer Science</OrgDivision><OrgName>CUNY Graduate Center</OrgName><OrgAddress><Street>365 Fifth Avenue</Street><Postcode>10016</Postcode><City>New York</City><State>NY</State><Country>USA</Country></OrgAddress></Affiliation><Affiliation ID="Aff17"><OrgID Level="Institution" Type="GRID">grid.5386.8</OrgID><OrgID Level="Institution" Type="ISNI">000000041936877X</OrgID><OrgDivision>Department of Mathematics</OrgDivision><OrgName>Cornell University</OrgName><OrgAddress><Street>545 Malott Hall</Street><Postcode>14853</Postcode><City>Ithaca</City><State>NY</State><Country>USA</Country></OrgAddress></Affiliation></EditorGroup></BookHeader><Chapter ID="Chap10" Language="En"><ChapterInfo ChapterType="OriginalPaper" ContainsESM="No" NumberingDepth="2" NumberingStyle="ContentOnly" TocLevels="0"><ChapterID>10</ChapterID><ChapterDOI>10.1007/978-3-642-35722-0_10</ChapterDOI><ChapterSequenceNumber>10</ChapterSequenceNumber><ChapterTitle Language="En">A Modal BI Logic for Dynamic Resource Properties</ChapterTitle><ChapterFirstPage>134</ChapterFirstPage><ChapterLastPage>148</ChapterLastPage><ChapterCopyright><CopyrightHolderName>Springer-Verlag Berlin Heidelberg</CopyrightHolderName><CopyrightYear>2013</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>978-3-642-35722-0</BookID><BookTitle>Logical Foundations of Computer Science</BookTitle></ChapterContext></ChapterInfo><ChapterHeader><AuthorGroup><Author AffiliationIDS="Aff18"><AuthorName DisplayOrder="Western"><GivenName>J.</GivenName><GivenName>R.</GivenName><FamilyName>Courtault</FamilyName></AuthorName></Author><Author AffiliationIDS="Aff18"><AuthorName DisplayOrder="Western"><GivenName>D.</GivenName><FamilyName>Galmiche</FamilyName></AuthorName></Author><Affiliation ID="Aff18"><OrgName>Université de Lorraine – LORIA UMR 7503, Campus Scientifique</OrgName><OrgAddress><Postbox>BP 239</Postbox><City>Vandœuvre-lès-Nancy</City><Country>France</Country></OrgAddress></Affiliation></AuthorGroup><Abstract ID="Abs1" Language="En"><Heading>Abstract</Heading><Para>The logic of Bunched implications (BI) and its variants or extensions provide a powerful framework to deal with resources having static properties. In this paper, we propose a modal extension of BI logic, called DBI, which allows us to deal with dynamic resource properties. After defining a Kripke semantics for DBI, we illustrate the interest of DBI for expressing some dynamic properties and then we propose a labelled tableaux calculus for this logic. This calculus is proved sound and complete w.r.t. the Kripke semantics. Moreover, we also give a method for countermodel generation in this logic.</Para></Abstract><ArticleNote Type="Misc"><SimplePara>This work is supported by the ANR grant DynRes on Dynamic Resources and Separation and Update Logics (project no. ANR-11-BS02-011).</SimplePara></ArticleNote></ChapterHeader><NoBody></NoBody></Chapter></Book></Series></Publisher><!-- Converted from LaTeX with LaTeX2A++ V3.1.37 --></istex:document></istex:metadataXml><mods version="3.6"><titleInfo lang="en"><title>A Modal BI Logic for Dynamic Resource Properties</title></titleInfo><titleInfo type="alternative" contentType="CDATA"><title>A Modal BI Logic for Dynamic Resource Properties</title></titleInfo><name type="personal"><namePart type="given">J.</namePart><namePart type="given">R.</namePart><namePart type="family">Courtault</namePart><affiliation>Université de Lorraine – LORIA UMR 7503, Campus Scientifique, BP 239, Vandœuvre-lès-Nancy, France</affiliation><role><roleTerm type="text">author</roleTerm></role></name><name type="personal"><namePart type="given">D.</namePart><namePart type="family">Galmiche</namePart><affiliation>Université de Lorraine – LORIA UMR 7503, Campus Scientifique, BP 239, Vandœuvre-lès-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">2013</dateIssued><copyrightDate encoding="w3cdtf">2013</copyrightDate></originInfo><language><languageTerm type="code" authority="rfc3066">en</languageTerm><languageTerm type="code" authority="iso639-2b">eng</languageTerm></language><abstract lang="en">Abstract: The logic of Bunched implications (BI) and its variants or extensions provide a powerful framework to deal with resources having static properties. In this paper, we propose a modal extension of BI logic, called DBI, which allows us to deal with dynamic resource properties. After defining a Kripke semantics for DBI, we illustrate the interest of DBI for expressing some dynamic properties and then we propose a labelled tableaux calculus for this logic. This calculus is proved sound and complete w.r.t. the Kripke semantics. Moreover, we also give a method for countermodel generation in this logic.</abstract><relatedItem type="host"><titleInfo><title>Logical Foundations of Computer Science</title><subTitle>International Symposium, LFCS 2013, San Diego, CA, USA, January 6-8, 2013. 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Foundations</topic></subject><identifier type="DOI">10.1007/978-3-642-35722-0</identifier><identifier type="ISBN">978-3-642-35721-3</identifier><identifier type="eISBN">978-3-642-35722-0</identifier><identifier type="ISSN">0302-9743</identifier><identifier type="eISSN">1611-3349</identifier><identifier type="BookTitleID">311175</identifier><identifier type="BookID">978-3-642-35722-0</identifier><identifier type="BookChapterCount">29</identifier><identifier type="BookVolumeNumber">7734</identifier><identifier type="BookSequenceNumber">7734</identifier><part><date>2013</date><detail type="volume"><number>7734</number><caption>vol.</caption></detail><extent unit="pages"><start>134</start><end>148</end></extent></part><recordInfo><recordOrigin>Springer-Verlag Berlin Heidelberg, 2013</recordOrigin></recordInfo></relatedItem><relatedItem type="series"><titleInfo><title>Lecture Notes in Computer Science</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 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