Distributive laws for concept lattices (Q1312172)

The central theme of this fascinating paper is an investigation of the connection between various types of distributive lattices and notions involving formal concept analysis as developed by R. Wille and his coworkers at Darmstadt. The paper is much too long and detailed to allow a detailed description of the results in this review. Suffice it to say that necessary and sufficient conditions are found for a concept lattice to be one of the following types: distributive, completely distributive, a frame, isomorphic to a topology, algebraic and completely distributive. Many other types of distributive lattices are characterized.