Composition of concept lattices

The theory of concept lattices is an efficient tool for knowledge discovery. The purpose of this paper is to discuss the composed lattice of two concept lattices with the same object set. We first define a pair of Galois connection between two posets obtained from two formal contexts, and discuss the properties of the Galois connection. Then, we define the composition of two concept lattices that have the same object set, and prove that it is a complete lattice. Finally, we discuss the relationship between the composed lattice and the concept lattice of the composed context, and prove that the composed lattice is a subset of the concept lattice of the composed context. Numerical example is employed to substantiate the theoretical arguments.