The Galois lattice as a hierarchical structure for topological relations
Identifieur interne : 004D03 ( Main/Merge ); précédent : 004D02; suivant : 004D04The Galois lattice as a hierarchical structure for topological relations
Auteurs : Amedeo Napoli [France] ; Florence Le Ber [France]Source :
- Annals of Mathematics and Artificial Intelligence [ 1012-2443 ] ; 2007-04-01.
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Abstract
Abstract: This paper presents the construction and the comparison of Galois lattices of topological relations for qualitative spatial representation and reasoning. The lattices rely on a correspondence between computational operations working on quantitative data, on the one hand, and topological relations working on qualitative knowledge units, on the other hand. After introducing the context of the present research work, i.e. the RCC-8 model of topological relations, we present computational operations for checking topological relations on spatial regions. From these operations are derived two sets of computational conditions that can be associated to topological relations through a Galois connection. The associated Galois lattices are presented and compared. Elements on the practical use of the lattices for representing spatial knowledge and for reasoning are also introduced and discussed.
Url:
- https://api.istex.fr/ark:/67375/VQC-2CWXZ7G8-G/fulltext.pdf
- https://hal.archives-ouvertes.fr/hal-00162171
DOI: 10.1007/s10472-007-9054-5
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active="#struct-300292" type="indirect"><org type="institution" xml:id="struct-300292" status="OLD"><orgName>Université Nancy 2</orgName><date type="end">2011-12-31</date><desc><address><addrLine>91 avenue de la Libération, BP 454, 54001 Nancy cedex</addrLine><country key="FR"></country></address></desc></org></tutelle><tutelle active="#struct-300293" type="indirect"><org type="institution" xml:id="struct-300293" status="OLD"><orgName>Institut National Polytechnique de Lorraine</orgName><orgName type="acronym">INPL</orgName><date type="end">2011-12-31</date><desc><address><country key="FR"></country></address></desc></org></tutelle><tutelle active="#struct-2496" type="direct"><org type="laboratory" xml:id="struct-2496" status="OLD"><orgName>INRIA Lorraine</orgName><desc><address><addrLine>615 rue du Jardin Botanique 54600 Villers-lès-Nancy</addrLine><country key="FR"></country></address><ref type="url">http://www.inria.fr/centre-de-recherche-inria/nancy-grand-est</ref></desc><listRelation><relation active="#struct-300009" type="direct"></relation></listRelation></org></tutelle></tutelles></hal:affiliation><country>France</country><placeName><settlement type="city">Nancy</settlement><region type="region" nuts="2">Grand Est</region><region type="old region" nuts="2">Lorraine (région)</region></placeName><orgName type="university">Université Nancy 2</orgName><orgName type="institution" wicri:auto="newGroup">Université de Lorraine</orgName><placeName><settlement type="city">Nancy</settlement><region type="region" nuts="2">Grand Est</region><region type="old region" nuts="2">Lorraine (région)</region></placeName><orgName type="university">Institut national polytechnique de Lorraine</orgName><orgName type="institution" wicri:auto="newGroup">Université de Lorraine</orgName></affiliation></author></analytic><idno type="DOI">10.1007/s10472-007-9054-5</idno><series><title level="j">Annals of Mathematics and Artificial Intelligence</title><idno type="ISSN">1012-2443</idno><imprint><date type="datePub">2007</date></imprint></series></biblStruct></sourceDesc></fileDesc><profileDesc><textClass><keywords scheme="mix" xml:lang="en"><term>Galois connection</term><term>Galois lattice</term><term>Hierarchical knowledge representation</term><term>Lattice-based classification</term><term>RCC-8</term><term>Topological relations</term></keywords></textClass></profileDesc></teiHeader><front><div type="abstract" xml:lang="en">This paper presents the construction and the comparison of Galois lattices of topological relations for qualitative spatial representation and reasoning. The lattices rely on a correspondence between computational operations working on quantitative data, on the one hand, and topological relations working on qualitative knowledge units, on the other hand. After introducing the context of the present research work, i.e. the RCC-8 model of topological relations, we present computational operations for checking topological relations on spatial regions. From these operations are derived two sets of computational conditions that can be associated to topological relations through a Galois connection. The associated Galois lattices are presented and compared. Elements on the practical use of the lattices for representing spatial knowledge and for reasoning are also introduced and discussed.</div></front></TEI></HAL><ISTEX><TEI wicri:istexFullTextTei="biblStruct"><teiHeader><fileDesc><titleStmt><title xml:lang="en">The Galois lattice as a hierarchical structure for topological relations</title><author><name sortKey="Napoli, Amedeo" sort="Napoli, Amedeo" uniqKey="Napoli A" first="Amedeo" last="Napoli">Amedeo Napoli</name></author><author><name sortKey="Le Ber, Florence" sort="Le Ber, Florence" uniqKey="Le Ber F" first="Florence" last="Le Ber">Florence Le Ber</name></author></titleStmt><publicationStmt><idno type="wicri:source">ISTEX</idno><idno type="RBID">ISTEX:B235EA0157A5C2CAF701F6F28C40BDD94E4EAF4E</idno><date when="2007" year="2007">2007</date><idno type="doi">10.1007/s10472-007-9054-5</idno><idno type="url">https://api.istex.fr/ark:/67375/VQC-2CWXZ7G8-G/fulltext.pdf</idno><idno type="wicri:Area/Istex/Corpus">002A22</idno><idno type="wicri:explorRef" wicri:stream="Istex" wicri:step="Corpus" wicri:corpus="ISTEX">002A22</idno><idno type="wicri:Area/Istex/Curation">002985</idno><idno type="wicri:Area/Istex/Checkpoint">000F54</idno><idno type="wicri:explorRef" wicri:stream="Istex" wicri:step="Checkpoint">000F54</idno><idno type="wicri:doubleKey">1012-2443:2007:Napoli A:the:galois:lattice</idno></publicationStmt><sourceDesc><biblStruct><analytic><title level="a" type="main" xml:lang="en">The Galois lattice as a hierarchical structure for topological relations</title><author><name sortKey="Napoli, Amedeo" sort="Napoli, Amedeo" uniqKey="Napoli A" first="Amedeo" last="Napoli">Amedeo Napoli</name><affiliation wicri:level="3"><country xml:lang="fr">France</country><wicri:regionArea>LORIA – UMR 7503, BP 239, 54506, Vandœuvre-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">Vandœuvre-lès-Nancy</settlement></placeName></affiliation><affiliation wicri:level="1"><country wicri:rule="url">France</country></affiliation></author><author><name sortKey="Le Ber, Florence" sort="Le Ber, Florence" uniqKey="Le Ber F" first="Florence" last="Le Ber">Florence Le Ber</name><affiliation wicri:level="3"><country xml:lang="fr">France</country><wicri:regionArea>LORIA – UMR 7503, BP 239, 54506, Vandœuvre-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">Vandœuvre-lès-Nancy</settlement></placeName></affiliation><affiliation wicri:level="3"><country xml:lang="fr">France</country><wicri:regionArea>CEVH, ENGEES, 1, Quai Koch, 67000, Strasbourg</wicri:regionArea><placeName><region type="region" nuts="2">Grand Est</region><region type="old region" nuts="2">Alsace (région administrative)</region><settlement type="city">Strasbourg</settlement></placeName></affiliation><affiliation wicri:level="1"><country wicri:rule="url">France</country></affiliation></author></analytic><monogr></monogr><series><title level="j">Annals of Mathematics and Artificial Intelligence</title><title level="j" type="abbrev">Ann Math Artif Intell</title><idno type="ISSN">1012-2443</idno><idno type="eISSN">1573-7470</idno><imprint><publisher>Springer Netherlands</publisher><pubPlace>Dordrecht</pubPlace><date type="published" when="2007-04-01">2007-04-01</date><biblScope unit="volume">49</biblScope><biblScope unit="issue">1-4</biblScope><biblScope unit="page" from="171">171</biblScope><biblScope unit="page" to="190">190</biblScope></imprint><idno type="ISSN">1012-2443</idno></series></biblStruct></sourceDesc><seriesStmt><idno type="ISSN">1012-2443</idno></seriesStmt></fileDesc><profileDesc><textClass><keywords scheme="KwdEn" xml:lang="en"><term>Galois connection</term><term>Galois lattice</term><term>Hierarchical knowledge representation</term><term>Lattice-based classification</term><term>RCC-8</term><term>Topological relations</term></keywords></textClass><langUsage><language ident="en">en</language></langUsage></profileDesc></teiHeader><front><div type="abstract" xml:lang="en">Abstract: This paper presents the construction and the comparison of Galois lattices of topological relations for qualitative spatial representation and reasoning. The lattices rely on a correspondence between computational operations working on quantitative data, on the one hand, and topological relations working on qualitative knowledge units, on the other hand. After introducing the context of the present research work, i.e. the RCC-8 model of topological relations, we present computational operations for checking topological relations on spatial regions. From these operations are derived two sets of computational conditions that can be associated to topological relations through a Galois connection. The associated Galois lattices are presented and compared. Elements on the practical use of the lattices for representing spatial knowledge and for reasoning are also introduced and discussed.</div></front></TEI></ISTEX></double></record>Pour manipuler ce document sous Unix (Dilib)
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