?url_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Adc&rft.title=A+theory+of+concepts+and+their+combinations+II%3A+A+Hilbert+space+representation&rft.creator=Aerts%2C+Diederik&rft.creator=Gabora%2C+Liane&rft.subject=Cognitive+Psychology&rft.subject=Philosophy+of+Mind&rft.subject=Artificial+Intelligence&rft.description=The+sets+of+contexts+and+properties+of+a+concept+are+embedded+in+the+complex+Hilbert+space+of+quantum+mechanics.+States+are+unit+vectors+or+density+operators%2C+and+contexts+and+properties+are+orthogonal+projections.+The+way+calculations+are+done+in+Hilbert+space+makes+it+possible+to+model+how+context+influences+the+state+of+a+concept.+Moreover%2C+a+solution+to+the+combination+of+concepts+is+proposed.+Using+the+tensor+product%2C+a+procedure+for+describing+combined+concepts+is+elaborated%2C+providing+a+natural+solution+to+the+pet+fish+problem.+This+procedure+allows+the+modeling+of+an+arbitrary+number+of+combined+concepts.+By+way+of+example%2C+a+model+for+a+simple+sentence+containing+a+subject%2C+a+predicate+and+an+object%2C+is+presented.+%0A&rft.publisher=Emerald&rft.contributor=Riegler%2C+Alexander&rft.date=2005&rft.type=Journal+(Paginated)&rft.type=PeerReviewed&rft.format=application%2Fpdf&rft.identifier=http%3A%2F%2Fcogprints.org%2F4771%2F1%2Fhvf2.pdf&rft.identifier=++Aerts%2C+Diederik+and+Gabora%2C+Liane++(2005)+A+theory+of+concepts+and+their+combinations+II%3A+A+Hilbert+space+representation.++%5BJournal+(Paginated)%5D+++++&rft.relation=http%3A%2F%2Fcogprints.org%2F4771%2F