We will start the tutorial by some general considerations on the relation of FCA and other knowledge representation formalisms, sketching structural similarities as well as unveiling diverging perspectives which in our opinion can be mutually inspiring.
We will proceed by introducing the basic notions of Formal Concept Analysis: formal contexts which essentially encode object-attribute correspondences and give rise to formal concepts which are defined to be pairs of intents (attribute combinations) and extents (sets of objects that are members of the described concept). Formal concepts allow a natural ordering resulting in a concept lattice. Due to the well known correspondence of lattices to closure systems and closure operators, the logic associated with this conceptual structure is that of attribute implications. All the introduced notions will be illustrated by instructive examples. We will demonstrate commonalities and differences of FCA compared to commonly known knowledge representation approaches like description logics.
In the sequel, we will present the algorithm of attribute exploration and its extension to the case of partial information. We transfer this method to an ontological setting by explaining how this algorithm can be coupled with reasoners in order to obtain an interactive method for ontology refinement where the expert involvement is minimized.
After having finished the introductory part of the tutorial, we will describe possible and existing applications of FCA in various Semantic Web settings, including ontology learning [2], engineering [3,4] and alignment [5].
We will conclude our tutorial with a demonstration of our tools, which implement the previously described approach. In a hands-on session, the participants will be given the opportunity to gain practical experience in using these tools within a concrete ontology engineering scenario.
[2] Cimiano, P., Hotho, A., Staab, S.: Learning concept hierarchies from text corpora using formal concept anaylsis. Journal of Artificial Intelligence Research (JAIR) 24 (2005) 305-339
[3] Völker, J., Rudolph, S.: Lexico-logical acquisition of OWL DL axioms - an integrated approach to ontology refinement. In Medina, R., Obiedkov, S., eds.: Proceedings of the 6th International Conference on Formal Concept Analysis (ICFCA). (2008) 62-77
[4] Völker, J., Rudolph, S.: Fostering Web Intelligence by Semi-automatic OWL Ontology Refinement In Proceedings of the 7th International Conference on Web Intelligence (WI). (2008), to appear (regular paper)
[5] Stumme, G., Mädche, A.: FCA-Merge: Bottom-up merging of ontologies. In: Proceedings of the 17th International Conference on Artificial Intelligence (IJCAI). (2001) 225-230