We propose an approach for extending both the terminological and the assertional part of a Description Logic knowledge base by using information provided by the knowledge base and by a domain expert. The use of techniques from Formal Concept Analysis ensures that, on the one hand, the interaction with the expert is kept to a minimum, and, on the other hand, we can show that the extended knowledge base is complete in a certain, well-defined sense.

@inproceedings{baader2007completing, author = {Baader, Franz and Ganter, Bernhard and Sertkaya, Baris and Sattler, Ulrike}, title = {Completing description logic knowledge bases using formal concept analysis}, booktitle = {Proceedings of the 20th international joint conference on Artifical intelligence}, publisher = {Morgan Kaufmann Publishers Inc.}, address = {San Francisco, CA, USA}, year = {2007}, pages = {230--235}, url = {http://dl.acm.org/citation.cfm?id=1625275.1625311}, keywords = {analysis, base, complete, concept, description, dl, fca, formal, knowledge, logic, ontology}, abstract = {We propose an approach for extending both the terminological and the assertional part of a Description Logic knowledge base by using information provided by the knowledge base and by a domain expert. The use of techniques from Formal Concept Analysis ensures that, on the one hand, the interaction with the expert is kept to a minimum, and, on the other hand, we can show that the extended knowledge base is complete in a certain, well-defined sense.} }

%0 = inproceedings %A = Baader, Franz and Ganter, Bernhard and Sertkaya, Baris and Sattler, Ulrike %B = Proceedings of the 20th international joint conference on Artifical intelligence %C = San Francisco, CA, USA %D = 2007 %I = Morgan Kaufmann Publishers Inc. %T = Completing description logic knowledge bases using formal concept analysis %U = http://dl.acm.org/citation.cfm?id=1625275.1625311

Given a finite set $C := C_1, C_n$ of description logic concepts, we are interested in computing the subsumption hierarchy of all least common subsumers of subsets of $C$ as well as the hierarchy of all conjunctions of subsets of $C$. These hierarchies can be used to support the bottom-up construction of description logic knowledge bases. The point is to compute the first hierarchy without having to compute the least common subsumer for all subsets of $C$, and the second hierarchy without having to check all possible pairs of such conjunctions explicitly for subsumption. We will show that methods from formal concept analysis developed for computing concept lattices can be employed for this purpose.

@inproceedings{baader2004applying, author = {Baader, Franz and Sertkaya, Baris}, title = {Applying Formal Concept Analysis to Description Logics.}, editor = {Eklund, Peter W.}, booktitle = {Concept Lattices}, series = {Lecture Notes in Computer Science}, publisher = {Springer}, address = {Berlin/Heidelberg}, year = {2004}, volume = {2961}, pages = {261--286}, url = {http://springerlink.metapress.com/openurl.asp?genre=article&issn=0302-9743&volume=2961&spage=261}, doi = {10.1007/978-3-540-24651-0_24}, isbn = {3-540-21043-1}, keywords = {analysis, concept, description, dl, fca, formal, logic, logics}, abstract = {Given a finite set $C := C_1, C_n$ of description logic concepts, we are interested in computing the subsumption hierarchy of all least common subsumers of subsets of $C$ as well as the hierarchy of all conjunctions of subsets of $C$. These hierarchies can be used to support the bottom-up construction of description logic knowledge bases. The point is to compute the first hierarchy without having to compute the least common subsumer for all subsets of $C$, and the second hierarchy without having to check all possible pairs of such conjunctions explicitly for subsumption. We will show that methods from formal concept analysis developed for computing concept lattices can be employed for this purpose.} }

%0 = inproceedings %A = Baader, Franz and Sertkaya, Baris %B = Concept Lattices %C = Berlin/Heidelberg %D = 2004 %I = Springer %T = Applying Formal Concept Analysis to Description Logics. %U = http://springerlink.metapress.com/openurl.asp?genre=article&issn=0302-9743&volume=2961&spage=261

@book{baader2003description,, title = {The description logic handbook: theory, implementation, and applications}, editor = {Baader, Franz and Calvanese, Diego and McGuinness, Deborah L. and Nardi, Daniele and Patel-Schneider, Peter F.}, publisher = {Cambridge University Press}, address = {New York, NY, USA}, year = {2003}, isbn = {0-521-78176-0}, keywords = {description, dl, logics} }

%0 = book %C = New York, NY, USA %D = 2003 %I = Cambridge University Press %T = The description logic handbook: theory, implementation, and applications

The OWL Web Ontology Language is a new formal language for representing ontologies in the Semantic Web. OWL has features from several families of representation languages, including primarily Description Logics and frames. OWL also shares many characteristics with RDF, the W3C base of the Semantic Web. In this paper, we discuss how the philosophy and features of OWL can be traced back to these older formalisms, with modifications driven by several other constraints on OWL. Several interesting problems have arisen where these influences on OWL have clashed.

@article{horrocks2003making, author = {Horrocks, Ian and Patel-Schneider, Peter F. and van Harmelen, Frank}, title = {From SHIQ and RDF to OWL: the making of a Web Ontology Language}, journal = {Web Semantics: Science, Services and Agents on the World Wide Web}, year = {2003}, volume = {1}, number = {1}, pages = {7-26}, url = {http://www.sciencedirect.com/science/article/pii/S1570826803000027}, doi = {10.1016/j.websem.2003.07.001}, issn = {1570-8268}, keywords = {dl, owl, rdf, semantic, web}, abstract = {The OWL Web Ontology Language is a new formal language for representing ontologies in the Semantic Web. OWL has features from several families of representation languages, including primarily Description Logics and frames. OWL also shares many characteristics with RDF, the W3C base of the Semantic Web. In this paper, we discuss how the philosophy and features of OWL can be traced back to these older formalisms, with modifications driven by several other constraints on OWL. Several interesting problems have arisen where these influences on OWL have clashed.} }

%0 = article %A = Horrocks, Ian and Patel-Schneider, Peter F. and van Harmelen, Frank %D = 2003 %T = From SHIQ and RDF to OWL: the making of a Web Ontology Language %U = http://www.sciencedirect.com/science/article/pii/S1570826803000027