Algebra System of Constrained Concept Lattice and its Completeness of Knowledge Representation

Concept lattice is an effective formal tool for data analysis and knowledge extraction. Constrained concept lattice is a new concept lattice structure which uses predicate logic to describe the user´s interesting background knowledge and merges the background knowledge into the process of concept lattice construction, so that the time and storage complexity of constructing concept lattice is reduced, and the utility and pertinence are improved for knowledge representation and knowledge extraction of concept lattice. In this paper, an algebra system of constrained concept lattice is constructed and its algebraic properties are presented. The completeness of knowledge representation of constrained concept lattice is proved, and hence the theoretical basis is provided for the application of constrained concept lattice.