Theoretical research on the distributed construction of concept lattices

The method of concept lattice building is one of the most important contents in the formal concept analysis. Concept lattice is corresponding with the formal context, so the distributed treatment of concept lattice certainly relates to some operations such as the decomposition and combination of context. This paper defines the horizontal and vertical combination operations in formal contexts and discusses three relations between same-field formal contexts, then especially present a novel similarity method to convert the inconsistent contexts into independent or consistent contexts. This paper also defines some basic operations among concepts and proves that the concept lattice of sub-contexts vertically combined is isomorphic to the union of sub-lattices of these sub-contexts in same-field and consistent contexts, which establishes the theoretical foundation for the distributed construction of concept lattices.