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In this paper, we show how the existence of taxonomies on objects and/or attributes can be used in Formal Concept Analysis to help discover generalized concepts.To that end, we analyze three generalization cases (∃, ∀, and α) and present different scenarios of a simultaneous generalization on both objects and attributes. We also discuss the cardinality of the generalized pattern set against the number of simple patterns produced from the initial data set.

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Double Boolean algebras are algebras (D, , , , , ⊥, ) of type (2, 2, 1, 1, 0, 0). They have been introduced to capture the equational theory of the algebra of protoconcepts. A filter (resp. an ideal) of a double Boolean algebra D is an upper set F (resp. down set I) closed under (resp. ). A filter F is called primary if F = ∅ and for all x ∈ D we have x ∈ F or x ∈ F . In this note we prove that if F is a filter and I an ideal such that F ∩ I = ∅ then there is a primary filter G containing F such that G ∩ I = ∅ (i.e. the Prime Ideal Theorem for double Boolean algebras).

Concept algebras are concept lattices enriched by a weak negation and a weak opposition. In Ganter and Kwuida (Contrib. Gen. Algebra, 14:63-72, 2004) we gave a contextual description of the lattice of weak negations on a finite lattice. In this contribution 1 we use this description to give a characterization of finite distributive concept algebras.

Abstract. Partially ordered sets labeled with k labels (k-posets) and their homomorphisms are examined. We give a representation of directed graphs by k-posets; this provides a new proof of the universality of the homomorphism order of k-posets. This universal order is a distributive lattice. We investigate some other properties, namely the infinite distributivity, the computation of infinite suprema and infima, and the complexity of certain decision problems involving the homomorphism order of k-posets. Sublattices are also examined.

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