Knowledge and Information Systems

, Volume 49, Issue 1, pp 171–195 | Cite as

Relationships between knowledge bases and related results

Regular Paper
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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.

Keywords

Knowledge base Knowledge reduction Dependency  Homomorphism Consistent mapping R-mapping Lattice 
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Notes

Acknowledgments

The authors would like to thank the editors and the anonymous reviewers for their valuable suggestions which have helped immensely in improving the quality of this paper. This work is supported by the National Natural Science Foundation of China (11461005, 11371130, 11371003, 11201490, 11401052), the Natural Science Foundation of Guangxi (2014GXNSFAA118001, 2012GX NSFGA060003), Guangxi University Science and Technology Research Project (KY2015YB075, KY2015YB081), Special Funds of Guangxi Distinguished Experts Construction Engineering and Key Laboratory of Optimization Control and Engineering Calculation in Department of Guangxi Education.

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Copyright information

© Springer-Verlag London 2015

Authors and Affiliations

  1. 1.College of ScienceGuangxi University for NationalitiesNanningPeople’s Republic of China
  2. 2.College of Mathematics and EconometricsHunan UniversityChangshaPeople’s Republic of China
  3. 3.College of Information and StatisticsGuangxi University of Finance and EconomicsNanningPeople’s Republic of China

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