Invited Speaker: Bernhard Ganter

Talk: Distributive Concept Algebras

What is the negation of a (formal) concept? There are several possible answers to this question. A rather simple one is to take the smallest concept that contains in its extent all objects which do not fall under the given concept. More formally, the weak negation of a formal concept (A,B) (of a formal context (G,M,I)) is defined as

$(A,B)^{\Delta}:=((G\setminus A)'',(G\setminus A)')$

The corresponding dual operation

$(A,B)^{\nabla}:=((M\setminus B)',(M\setminus B)'')$

is called the weak opposition, and a concept algebra is a concept lattice together with these two operations.

These notions were introduced by Rudolf Wille, who also started to investigate the mathematical theory of concept algebras. Recently, some progress in these investigations was made by Léonard Kwuida and the author. We now have some insight in the structure of at least the finite distributive concept algebras.

Biography

Bernhard Ganter is professor of mathematics at Technische Universität Dresden (the University of Dresden, Germany), where he is also the Head of the Algebra Institute. He has received his academic degrees some thirty years ago under the supervision of Rudolf Wille in Darmstadt. He is co-author of the first textbook on Formal Concept Analysis.

Contact

E-Mail: ganter@math.tu-dresden.de