Formal Concept Analysis as Mathematical Theory of Concepts and Concept Hierarchies

Abstract

Formal Concept Analysis has been originally developed as a subfield of Applied Mathematics based on the mathematization of concept and concept hierarchy. Only after more than a decade of de- velopment, the connections to the philosophical logic of human thought became clearer and even later the connections to Piaget’s cognitive struc- turalism which Thomas Bernhard Seiler convincingly elaborated to a comprehensive theory of concepts in his recent book [Se01]. It is the main concern of this paper to show the surprisingly rich correspondences be- tween Seiler’s multifarious aspects of concepts in the human mind and the structural properties and relationships of formal concepts in Formal Concept Analysis. These correspondences make understandable, what has been experienced in a great multitude of applications, that Formal Concept Analysis may function in the sense of transdisciplinary mathe- matics, i.e., it allows mathematical thought to aggregate with other ways of thinking and thereby to support human thought and action. 1