Formal Concept Analysis - Overview and History

Overview and History

The original motivation of formal concept analysis was the concrete representation of complete lattices and their properties by means of formal contexts, data tables that represent binary relations between objects and attributes. In this theory, a formal concept is defined to a pair consisting of a set of objects (the "extent") and a set of attributes (the "intent") such that the extent consists of all objects that share the given attributes, and the intent consists of all attributes shared by the given objects. In this way, formal concept analysis formalizes the notions of extension and intension.

Pairs of formal concepts may be partially ordered by the subset relation between their sets of objects, or equivalently by the superset relation between their sets of attributes. This ordering results in a graded system of sub- and superconcepts, a concept hierarchy, which can be displayed as a line diagram. The family of these concepts obeys the mathematical axioms defining a lattice, and is called more formally a concept lattice. In French this is called a treillis de Galois (Galois lattice) because of the relation between the sets of concepts and attributes is a Galois connection.

The theory in its present form goes back to the Darmstadt research group led by Rudolf Wille, Bernhard Ganter and Peter Burmeister, where formal concept analysis originated in the early 1980s. The mathematical basis, however, was already created by Garrett Birkhoff in the 1930s as part of the general lattice theory. Before the work of the Darmstadt group, there were already approaches in various French groups. Philosophical foundations of formal concept analysis refer in particular to Charles S. Peirce and the educationalist Hartmut von Hentig.