Other

1997

The ``Formal Concept Analysis'' project was born around 1980, when a re�search group in Darmstadt, Germany, begun to systematically develop a frame�work for lattice theory applications. It was first presented to the mathematical re�search g public in a programmatic lecture given at the 1981 Banff conference on Ordered Sets [5]. Since then, several hundred articles [1] have been published, includin g a textbook on the mathematical foundations [2]. The Darmstadt group alone has participated in more than a hundred application cooperation projects. For�mer members of that team have founded a small firm and now make their living from such applications. The sophisticated name of ``Formal Concept Analysis'' needs to be explained. The method is mainly used for the analysis of data, i.e. for investigating and processing explicitly given information. Such data will be structured into units which are formal abstractions of concepts of human thought allowing meaningful and comprehensible interpretation. We use the prefix formal to emphasize that these formal concepts are mathematical entities and must not be identified with concepts of the mind. The same prefix indicates that the basic data format, that of a formal context, is merely a formalization that encodes only a small portion of what is usually referred to as a ``context''. Much of the mathematics required for the applications has been borrowed directly from lattice theory. The basic construction of a complete lattice from a binary relation is explained already in the first edition of Birkhoff's Lattic e Theory. But the new goal made it also necessary to extend and to smoothen the theory. Thereby, Formal Concept Analysis has created results that may be of interest even without considering the applications by which they were motivated. For proofs, citations, and further details we refer to [2].