?url_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Adc&rft.title=The+Algebraic+Structure+of+Sets+of+Regions&rft.creator=Stell%2C+J.+G.&rft.creator=Worboys%2C+M.+F.&rft.subject=Artificial+Intelligence&rft.description=The+provision+of+ontologies+for+spatial+entities+is+an+important+topic+in+spatial+information+theory.+Heyting+algebras%2C+co-Heyting+algebras%2C+and+bi-Heyting+algebras+are+structures+having+considerable+potential+for+the+theoretical+basis+of+these+ontologies.+This+paper+gives+an+introduction+to+these+Heyting+structures%2C+and+provides+evidence+of+their+importance+as+algebraic+theories+of+sets+of+regions.+The+main+evidence+is+a+proof+that+elements+of+certain+Heyting+algebras+provide+models+of+the+Region-Connection+Calculus+developed+by+Cohn+et+al.+By+using+the+mathematically+well+known+techniques+of+%60%60pointless+topology''%2C+it+is+straightforward+to+conduct+this+proof+without+any+need+to+assume+that+regions+consist+of+sets+of+points.+Further+evidence+is+provided+by+a+new+qualitative+theory+of+regions+with+indeterminate+boundaries.+This+theory+uses+modal+operators+which+are+related+to+the+algebraic+operations+present+in+a+bi-Heyting+algebra.&rft.publisher=Lecture+Notes+in+Computer+Science%2C+volume+1329%2C+Springer+Verlag%2C+Berlin&rft.contributor=Hirtle%2C+S.+C.&rft.contributor=Frank%2C+A.+U.&rft.date=1997&rft.type=Conference+Paper&rft.type=NonPeerReviewed&rft.format=application%2Fpostscript&rft.identifier=http%3A%2F%2Fcogprints.org%2F517%2F2%2Fcosit-97.ps&rft.identifier=++Stell%2C+J.+G.+and+Worboys%2C+M.+F.++(1997)+The+Algebraic+Structure+of+Sets+of+Regions.++%5BConference+Paper%5D+++++&rft.relation=http%3A%2F%2Fcogprints.org%2F517%2F