Among many other knowledge representations formalisms, Ontologies
d Formal Concept Analysis (FCA) aim at modeling 'concepts'. We
scuss how these two formalisms may complement another from an
plication point of view. In particular, we will see how FCA can
used to support Ontology Engineering, and how ontologies can be
ploited in FCA applications. The interplay of FCA and ontologies
studied along the life cycle of an ontology:
i) FCA can support the building of the ontology as a
earning technique.
ii) The established ontology can be analyzed and navigated by
sing techniques of FCA.
iii) Last but not least, the ontology may be used to improve an FCA
pplication.

In the last years, the main orientation of Formal Concept Analysis
(FCA) has turned from mathematics towards computer science. This
article provides a review of this new orientation and analyzes why
and how FCA and computer science attracted each other. It discusses
FCA as a knowledge representation formalism using five knowledge
representation principles provided by Davis, Shrobe, and Szolovits
(1993). It then studies how and why mathematics-based researchers
got attracted by computer science. We will argue for continuing this
trend by integrating the two research areas FCA and Ontology Engineering.
The second part of the article discusses three lines of research which
witness the new orientation of Formal Concept Analysis: FCA as a
conceptual clustering technique and its application for supporting
the merging of ontologies; the efficient computation of association
rules and the structuring of the results; and the visualization and
management of conceptual hierarchies and ontologies including its
application in an email management system.