141 Novi Sad J. Math. Vol. 34, No. 2, 2004, 141-152 Proc. Novi Sad Algebraic Conf. 2003 (eds. I. Dolinka, A. Tepavˇ cevi´ c) CONGRUENCES OF CONCEPT ALGEBRAS 1 L´ eonard Kwuida 2 Abstract. Concept algebras are concept lattices enriched with two unary operations, a weak negation and a weak opposition. In this contribution we provide a characterization of congruences of concept algebras. AMS Mathematics Subject Classification (2000): 06B10, 06B05, 03G25, 03G10 Key words and phrases: Formal Concept Analysis, Contextual Logic, negation, concept algebras, weakly dicomplemented lattices, complete congruences 1. Introduction Concept algebras arise from the need to develop a Contextual Boolean Logic, based on “concept as unit of thought”. A concept is considered to be determined by its extent and its intent. The extent consists of all entities belonging to the concept, whilst the intent is the set of properties shared by these entities. The notion of concept has been formalized at the early 80s ([Wi82]) and led to the theory of Formal Concept Analysis ([GW99]). A formal context is a triple (G,M,I ) of sets such that I ⊆ G × M . The members of G are called objects and those of M attributes. If (g,m) ∈ I the object g is said to have m as an attribute. For subsets A ⊆ G and B ⊆ M , A ′ and B ′ are defined by A ′ := {m ∈ M |∀g ∈ A gIm} B ′ := {g ∈ G |∀m ∈ B gIm}. The operation ′ , usually called derivation, induces a Galois connection between the powersets of G and of M . If different relations are defined on the same sets we use other notations to avoid confusion. A formal concept of the context (G,M,I ) is a pair (A, B) with A ⊆ G and B ⊆ M such that A ′ = B and B ′ = A. A is called the extent and B the intent of the concept (A, B). B(G,M,I ) denotes the set of all formal concepts 1 partially supported by GrK 334 of the German Research Foundation 2 Institut f¨ ur Algebra, Technische Universit¨at Dresden, D-01062 Dresden, e-mail: kwuida@math.tu-dresden.de