Roughening the $\mathcal{EL}$ Envelope
Identifieur interne : 003659 ( Istex/Corpus ); précédent : 003658; suivant : 003660Roughening the $\mathcal{EL}$ Envelope
Auteurs : Rafael Pe Aloza ; Tingting ZouSource :
- Lecture Notes in Computer Science [ 0302-9743 ]
Abstract
Abstract: The $\mathcal{EL}$ family of description logics (DLs) has been successfully applied for representing the knowledge of several domains, specially from the bio-medical fields. One of its principal characteristics is that its reasoning tasks have polynomial complexity, which makes them suitable for large-scale knowledge bases. In their classical form, description logics cannot handle imprecise concepts in a satisfactory manner. Rough sets have been studied as a method for describing imprecise notions, by providing a lower and an upper approximation, which are defined through classes of indiscernible elements. In this paper we study the combination of the $\mathcal{EL}$ family of DLs with the notion of rough sets, thus obtaining a family of rough DLs. We show that the rough extension of these DLs maintains the polynomial-time complexity enjoyed by its classical counterpart. We also present a completion-based algorithm that is a strict generalization of the known method for the DL $\mathcal{EL}^{++}$ .
Url:
DOI: 10.1007/978-3-642-40885-4_6
Links to Exploration step
ISTEX:E397B373C4098C1D55AF6B2BCB8EC57201D340C5Le document en format XML
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$\mathcal{EL}$
</formula> Envelope</title><author><name sortKey="Pe Aloza, Rafael" sort="Pe Aloza, Rafael" uniqKey="Pe Aloza R" first="Rafael" last="Pe Aloza">Rafael Pe Aloza</name><affiliation><mods:affiliation>Theoretical Computer Science, TU Dresden Center for Advancing Electronics Dresden, Germany</mods:affiliation></affiliation><affiliation><mods:affiliation>E-mail: penaloza@tcs.inf.tu-dresden.de</mods:affiliation></affiliation></author><author><name sortKey="Zou, Tingting" sort="Zou, Tingting" uniqKey="Zou T" first="Tingting" last="Zou">Tingting Zou</name><affiliation><mods:affiliation>College of Computer Science and Technology, Jilin University, China</mods:affiliation></affiliation><affiliation><mods:affiliation>E-mail: zoutingt@163.com</mods:affiliation></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></textClass></profileDesc></teiHeader><front><div type="abstract" xml:lang="en">Abstract: The $\mathcal{EL}$ family of description logics (DLs) has been successfully applied for representing the knowledge of several domains, specially from the bio-medical fields. One of its principal characteristics is that its reasoning tasks have polynomial complexity, which makes them suitable for large-scale knowledge bases. In their classical form, description logics cannot handle imprecise concepts in a satisfactory manner. Rough sets have been studied as a method for describing imprecise notions, by providing a lower and an upper approximation, which are defined through classes of indiscernible elements. In this paper we study the combination of the $\mathcal{EL}$ family of DLs with the notion of rough sets, thus obtaining a family of rough DLs. We show that the rough extension of these DLs maintains the polynomial-time complexity enjoyed by its classical counterpart. 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One of its principal characteristics is that its reasoning tasks have polynomial complexity, which makes them suitable for large-scale knowledge bases. In their classical form, description logics cannot handle imprecise concepts in a satisfactory manner. Rough sets have been studied as a method for describing imprecise notions, by providing a lower and an upper approximation, which are defined through classes of indiscernible elements. In this paper we study the combination of the $\mathcal{EL}$ family of DLs with the notion of rough sets, thus obtaining a family of rough DLs. We show that the rough extension of these DLs maintains the polynomial-time complexity enjoyed by its classical counterpart. 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type="first">Oscar</forename><surname>Nierstrasz</surname></persName><affiliation><idno type="GRID" subtype="Institution">grid.5734.5</idno><idno type="ISNI" subtype="Institution">0000000107265157</idno><orgName type="institution">University of Bern</orgName><address><settlement>Bern</settlement><country key="CH">SWITZERLAND</country></address></affiliation></editor><editor><persName><forename type="first">C.</forename><surname>Pandu Rangan</surname></persName><affiliation><idno type="GRID" subtype="Institution">grid.417969.4</idno><idno type="ISNI" subtype="Institution">0000000123151926</idno><orgName type="institution">Indian Institute of Technology</orgName><address><settlement>Madras</settlement><country key="IN">INDIA</country></address></affiliation></editor><editor><persName><forename type="first">Bernhard</forename><surname>Steffen</surname></persName><affiliation><idno type="GRID" subtype="Institution">grid.5675.1</idno><idno type="ISNI" subtype="Institution">0000000104169637</idno><orgName type="institution">University of Dortmund</orgName><address><settlement>Dortmund</settlement><country key="DE">GERMANY</country></address></affiliation></editor><editor><persName><forename type="first">Madhu</forename><surname>Sudan</surname></persName><affiliation><idno type="GRID" subtype="Institution">grid.116068.8</idno><idno type="ISNI" subtype="Institution">0000000123412786</idno><orgName type="institution">Massachusetts Institute of Technology</orgName><address><region>MA</region><country key="US">UNITED STATES</country></address></affiliation></editor><editor><persName><forename type="first">Demetri</forename><surname>Terzopoulos</surname></persName><affiliation><idno type="GRID" subtype="Institution">grid.19006.3e</idno><idno type="ISNI" subtype="Institution">0000000096326718</idno><orgName type="institution">University of California</orgName><address><settlement>Los Angeles</settlement><region>CA</region><country key="US">UNITED STATES</country></address></affiliation></editor><editor><persName><forename type="first">Doug</forename><surname>Tygar</surname></persName><affiliation><idno type="GRID" subtype="Institution">grid.47840.3f</idno><idno type="ISNI" subtype="Institution">0000000121817878</idno><orgName type="institution">University of California</orgName><address><settlement>Berkeley</settlement><region>CA</region><country key="US">UNITED STATES</country></address></affiliation></editor><editor><persName><forename type="first">Moshe</forename><forename type="first">Y.</forename><surname>Vardi</surname></persName><affiliation><idno type="GRID" subtype="Institution">grid.21940.3e</idno><idno type="ISNI" subtype="Institution"> 0000000419368278</idno><orgName type="institution">Rice 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 <formula xml:id="IEq2" notation="TEX"><media mimeType="image" url=""></media>
$\mathcal{EL}$
</formula> family of description logics (DLs) has been successfully applied for representing the knowledge of several domains, specially from the bio-medical fields. One of its principal characteristics is that its reasoning tasks have polynomial complexity, which makes them suitable for large-scale knowledge bases. In their classical form, description logics cannot handle imprecise concepts in a satisfactory manner. Rough sets have been studied as a method for describing imprecise notions, by providing a lower and an upper approximation, which are defined through classes of indiscernible elements.</p><p>In this paper we study the combination of the <formula xml:id="IEq3" notation="TEX"><media mimeType="image" url=""></media>
$\mathcal{EL}$
</formula> family of DLs with the notion of rough sets, thus obtaining a family of rough DLs. We show that the rough extension of these DLs maintains the polynomial-time complexity enjoyed by its classical counterpart. We also present a completion-based algorithm that is a strict generalization of the known method for the DL <formula xml:id="IEq4" notation="TEX"><media mimeType="image" url=""></media>
$\mathcal{EL}^{++}$
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TocLevels="0"><ChapterID>6</ChapterID><ChapterDOI>10.1007/978-3-642-40885-4_6</ChapterDOI><ChapterSequenceNumber>6</ChapterSequenceNumber><ChapterTitle Language="En">Roughening the <InlineEquation ID="IEq1"><InlineMediaObject><ImageObject Color="BlackWhite" FileRef="978-3-642-40885-4_6_Chapter_TeX2GIF_IEq1.gif" Format="GIF" Rendition="HTML" Type="Linedraw"></ImageObject></InlineMediaObject><EquationSource Format="TEX">$\mathcal{EL}$</EquationSource></InlineEquation> Envelope</ChapterTitle><ChapterFirstPage>71</ChapterFirstPage><ChapterLastPage>86</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><PartID>4</PartID><BookID>978-3-642-40885-4</BookID><BookTitle>Frontiers of Combining Systems</BookTitle></ChapterContext></ChapterInfo><ChapterHeader><AuthorGroup><Author AffiliationIDS="Aff22"><AuthorName DisplayOrder="Western"><GivenName>Rafael</GivenName><FamilyName>Peñaloza</FamilyName></AuthorName><Contact><Email>penaloza@tcs.inf.tu-dresden.de</Email></Contact></Author><Author AffiliationIDS="Aff23"><AuthorName DisplayOrder="Western"><GivenName>Tingting</GivenName><FamilyName>Zou</FamilyName></AuthorName><Contact><Email>zoutingt@163.com</Email></Contact></Author><Affiliation ID="Aff22"><OrgDivision>Theoretical Computer Science</OrgDivision><OrgName>TU Dresden Center for Advancing Electronics Dresden</OrgName><OrgAddress><Country>Germany</Country></OrgAddress></Affiliation><Affiliation ID="Aff23"><OrgID Level="Institution" Type="GRID">grid.64924.3d</OrgID><OrgID Level="Institution" Type="ISNI">0000000417605735</OrgID><OrgDivision>College of Computer Science and Technology</OrgDivision><OrgName>Jilin University</OrgName><OrgAddress><Country>China</Country></OrgAddress></Affiliation></AuthorGroup><Abstract ID="Abs1" Language="En"><Heading>Abstract</Heading><Para>The <InlineEquation ID="IEq2"><InlineMediaObject><ImageObject Color="BlackWhite" FileRef="978-3-642-40885-4_6_Chapter_TeX2GIF_IEq2.gif" Format="GIF" Rendition="HTML" Type="Linedraw"></ImageObject></InlineMediaObject><EquationSource Format="TEX">$\mathcal{EL}$</EquationSource></InlineEquation> family of description logics (DLs) has been successfully applied for representing the knowledge of several domains, specially from the bio-medical fields. One of its principal characteristics is that its reasoning tasks have polynomial complexity, which makes them suitable for large-scale knowledge bases. In their classical form, description logics cannot handle imprecise concepts in a satisfactory manner. Rough sets have been studied as a method for describing imprecise notions, by providing a lower and an upper approximation, which are defined through classes of indiscernible elements.</Para><Para>In this paper we study the combination of the <InlineEquation ID="IEq3"><InlineMediaObject><ImageObject Color="BlackWhite" FileRef="978-3-642-40885-4_6_Chapter_TeX2GIF_IEq3.gif" Format="GIF" Rendition="HTML" Type="Linedraw"></ImageObject></InlineMediaObject><EquationSource Format="TEX">$\mathcal{EL}$</EquationSource></InlineEquation> family of DLs with the notion of rough sets, thus obtaining a family of rough DLs. We show that the rough extension of these DLs maintains the polynomial-time complexity enjoyed by its classical counterpart. We also present a completion-based algorithm that is a strict generalization of the known method for the DL <InlineEquation ID="IEq4"><InlineMediaObject><ImageObject Color="BlackWhite" FileRef="978-3-642-40885-4_6_Chapter_TeX2GIF_IEq4.gif" Format="GIF" Rendition="HTML" Type="Linedraw"></ImageObject></InlineMediaObject><EquationSource Format="TEX">$\mathcal{EL}^{++}$</EquationSource></InlineEquation>.</Para></Abstract></ChapterHeader><NoBody></NoBody></Chapter></Part></Book></Series></Publisher><!-- Converted from LaTeX with LaTeX2A++ V3.1.38 --></istex:document></istex:metadataXml><mods version="3.6"><titleInfo lang="en"><title>Roughening the $\mathcal{EL}$ Envelope</title></titleInfo><titleInfo type="alternative" contentType="CDATA"><title>Roughening the $\mathcal{EL}$ Envelope</title></titleInfo><name type="personal"><namePart type="given">Rafael</namePart><namePart type="family">Peñaloza</namePart><affiliation>Theoretical Computer Science, TU Dresden Center for Advancing Electronics Dresden, Germany</affiliation><affiliation>E-mail: penaloza@tcs.inf.tu-dresden.de</affiliation><role><roleTerm type="text">author</roleTerm></role></name><name type="personal"><namePart type="given">Tingting</namePart><namePart type="family">Zou</namePart><affiliation>College of Computer Science and Technology, Jilin University, China</affiliation><affiliation>E-mail: zoutingt@163.com</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 $\mathcal{EL}$ family of description logics (DLs) has been successfully applied for representing the knowledge of several domains, specially from the bio-medical fields. One of its principal characteristics is that its reasoning tasks have polynomial complexity, which makes them suitable for large-scale knowledge bases. In their classical form, description logics cannot handle imprecise concepts in a satisfactory manner. Rough sets have been studied as a method for describing imprecise notions, by providing a lower and an upper approximation, which are defined through classes of indiscernible elements. In this paper we study the combination of the $\mathcal{EL}$ family of DLs with the notion of rough sets, thus obtaining a family of rough DLs. We show that the rough extension of these DLs maintains the polynomial-time complexity enjoyed by its classical counterpart. We also present a completion-based algorithm that is a strict generalization of the known method for the DL $\mathcal{EL}^{++}$ .</abstract><relatedItem type="host"><titleInfo><title>Frontiers of Combining Systems</title><subTitle>9th International Symposium, FroCoS 2013, Nancy, France, September 18-20, 2013. 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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 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type="family">Fontaine</namePart><affiliation>LORIA, Inria Nancy Grand Est, Université de Lorraine, 615 rue du Jardin Botanique, 54602, Villers-les-Nancy, France</affiliation><affiliation>E-mail: pascal.fontaine@inria.fr</affiliation><role><roleTerm type="text">editor</roleTerm></role></name><name type="personal"><namePart type="given">Christophe</namePart><namePart type="family">Ringeissen</namePart><affiliation>LORIA, Inria Nancy Grand Est, 615 rue du Jardin Botanique, 54602, Villers-lès-Nancy, France</affiliation><affiliation>E-mail: christophe.ringeissen@loria.fr</affiliation><role><roleTerm type="text">editor</roleTerm></role></name><name type="personal"><namePart type="given">Renate</namePart><namePart type="given">A.</namePart><namePart type="family">Schmidt</namePart><affiliation>School of Computer Science, The University of Manchester, Oxford Rd, Kilburn Building, M13 9PL, Manchester, UK</affiliation><affiliation>E-mail: renate.schmidt@manchester.ac.uk</affiliation><role><roleTerm type="text">editor</roleTerm></role></name><genre type="sub-series"></genre><identifier type="ISSN">0302-9743</identifier><identifier type="eISSN">1611-3349</identifier><identifier type="SubSeriesID">1244</identifier></relatedItem><identifier type="ISSN">0302-9743</identifier><identifier type="eISSN">1611-3349</identifier><identifier type="SeriesID">558</identifier><recordInfo><recordOrigin>Springer-Verlag Berlin Heidelberg, 2013</recordOrigin></recordInfo></relatedItem><identifier type="istex">E397B373C4098C1D55AF6B2BCB8EC57201D340C5</identifier><identifier type="ark">ark:/67375/HCB-169HDHTS-2</identifier><identifier type="DOI">10.1007/978-3-642-40885-4_6</identifier><identifier type="ChapterID">6</identifier><identifier type="ChapterID">Chap6</identifier><accessCondition type="use and reproduction" contentType="copyright">Springer-Verlag Berlin Heidelberg, 2013</accessCondition><recordInfo><recordContentSource 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