Abstract
Relationships between information systems are very important topics in the field of artificial intelligence. The concept of homomorphisms is an effective mathematical tool to study relationships between information systems. A knowledge base is a special relation information system. This paper investigates invariant characteristics of knowledge bases under the homomorphism. The fact that knowledge bases themselves are invariant and inverse invariant under the homomorphism is firstly proved. Next, some invariant characteristics and inverse invariant characteristics under the homomorphism, such as the dependency of knowledge bases, knowledge reductions, coordinate families and necessary relations, are obtained based on this fact. Finally, lattice characteristics of the dependency of knowledge bases are given. These results will be significant for establishing a framework of granular computing in knowledge bases.
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