Algorithms for Merging Probabilistic Knowledge Bases

  • Van Tham NguyenEmail author
  • Ngoc Thanh Nguyen
  • Trong Hieu Tran
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11431)


There is an increasing need to develop appropriate techniques for merging probabilistic knowledge bases (PKB) in knowledge-based systems. To deal with merging problems, several approaches have been put forward. However, in the proposed models, the representation of the merged probabilistic knowledge base is not similar to the representation of original knowledge bases. The drawback of the solutions is that probabilistic constraints on the set of input knowledge bases must have the same structure and there is no algorithm for implementing the merging process. In this paper, we proposed two algorithms for merging probabilistic knowledge bases represented by various structures. To this aim, the method of constraint deduction is investigated, a set of mean merging operators is proposed and several desirable logical properties are presented and discussed. These are the basis for building algorithms. The complexity of algorithms as well as related propositions are also analysised and discussed.


Probabilistic knowledge bases Merging operator Merging algorithms 



This study was fully supported by Science and Technology Development Fund from Vietnam National University, Hanoi (VNU) under grant number QG.19.23 (2019-2020). The authors would like to thank Professor Quang Thuy Ha and Knowledge Technology and Data Science Lab, Faculty of Information Technology, VNU - University of Engineering and Technology for expertise support.


  1. 1.
    Bloch, I., et al.: Fusion: general concepts and characteristics. Int. J. Intell. Syst. 16(10), 1107–1134 (2001)CrossRefGoogle Scholar
  2. 2.
    Potyka, N., Thimm, M.: Consolidation of probabilistic knowledge bases by inconsistency minimization. In: Proceedings ECAI 2014, pp. 729–734. IOS Press (2014)Google Scholar
  3. 3.
    Potyka, N., Thimm, M.: Probabilistic reasoning with inconsistent beliefs using inconsistency measures. In: International Joint Conference on Artificial Intelligence 2015 (IJCAI 2015), pp. 3156–3163. AAAI Press (2015)Google Scholar
  4. 4.
    Potyka, N.: Solving Reasoning Problems for Probabilistic Conditional Logics with Consistent and Inconsistent Information. FernUniversitat, Hagen (2016)Google Scholar
  5. 5.
    Nguyen, V.T., Tran, T.H.: Inconsistency measures for probabilistic knowledge bases. In: Proceedings KSE 2017, pp. 148–153. IEEE Xplore (2017)Google Scholar
  6. 6.
    Nguyen, V.T., Tran, T.H.: Solving inconsistencies in probabilistic knowledge bases via inconsistency measures. In: Nguyen, N.T., Hoang, D.H., Hong, T.-P., Pham, H., Trawiński, B. (eds.) ACIIDS 2018. LNCS (LNAI), vol. 10751, pp. 3–14. Springer, Cham (2018). Scholar
  7. 7.
    Nguyen, V.T., Nguyen, N.T., Tran, T.H., Nguyen, D.K.L.: Method for restoring consistency in probabilistic knowledge bases. J. Cybern. Syst. 1–22 (2018)Google Scholar
  8. 8.
    Nguyen, N.T.: Advanced Methods for Inconsistent Knowledge Management, pp. 1–351. Springer, Heidelberg (2008). Scholar
  9. 9.
    Genest, C., Zidek, J.V.: Combining probability distributions: a critique and an annotated bibliography. Stat. Sci. 1, 114–135 (1986)MathSciNetCrossRefGoogle Scholar
  10. 10.
    Dempster, A.P.: Upper and lower probabilities induced by a multivalued mapping. In: Yager, R.R., Liu, L. (eds.) Classic Works of the Dempster-Shafer Theory of Belief Functions, vol. 219, pp. 52–72. Springer, Heidelberg (2008). Scholar
  11. 11.
    Levy, W.B., Deliç, H.: Maximum entropy aggregation of individual opinions. IEEE Trans. Syst. Man Cybern. 24(4), 606–613 (1994)MathSciNetCrossRefGoogle Scholar
  12. 12.
    Kern-Isberner, G.: Conditionals in Nonmonotonic Reasoning and Belief Revision. LNCS (LNAI), vol. 2087. Springer, Heidelberg (2001). Scholar
  13. 13.
    Kern-Isberner, G., Rödder, W.: Belief revision and information fusion on optimum entropy. Int. J. Intell. Syst. 19(9), 837–857 (2004)CrossRefGoogle Scholar
  14. 14.
    Kern-Isberner, G., Wilhelm, M., Beierle, C.: Probabilistic knowledge representation using the principle of maximum entropy and Gröbner basis theory. Ann. Math. Artif. Intell. 79(1–3), 163–179 (2017)MathSciNetCrossRefGoogle Scholar
  15. 15.
    Nguyen, N.T.: Methods for Consensus Choice and their Applications in Conflict Resolving in Distributed Systems. Wroclaw University of Technology Press (2002). (in Polish)Google Scholar
  16. 16.
    Vomlel, J.: Methods of probabilistic knowledge integration. Ph.D. thesis, Czech Technical University, Prague (1999)Google Scholar
  17. 17.
    Wilmers, G.: The social entropy process: axiomatising the aggregation of probabilistic beliefs. In: Probability, Uncertainty and Rationality (2010)Google Scholar
  18. 18.
    Adamcík, M., Wilmers, G.: The irrelevant information principle for collective probabilistic reasoning. Kybernetika 50(2), 175–188 (2014)MathSciNetzbMATHGoogle Scholar
  19. 19.
    Adamcik, M.: Collective reasoning under uncertainty and inconsistency. Ph.D. thesis, University of Manchester, UK (2014)Google Scholar
  20. 20.
    Nguyen, V.T., Nguyen, N.T., Tran, T.H.: Framework for merging probabilistic knowledge bases. In: Nguyen, N.T., Pimenidis, E., Khan, Z., Trawiński, B. (eds.) ICCCI 2018. LNCS (LNAI), vol. 11055, pp. 31–42. Springer, Cham (2018). Scholar
  21. 21.
    Achs, Á., Kiss, A.: Fixed point query in fuzzy datalog Programs. In: Annales Univ. Sci. Budapest, Sect., no. 15, pp. 223–231 (1995)Google Scholar
  22. 22.
    Achs, Á., Kiss, A.: Fuzzy extension of datalog. Acta Cybern. 12(2), 153–166 (1995)MathSciNetzbMATHGoogle Scholar
  23. 23.
    Achs, Á.: A multivalued knowledge-base model. CoRR, abs/1003.1658 (2010)Google Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Van Tham Nguyen
    • 1
    • 3
    Email author
  • Ngoc Thanh Nguyen
    • 2
  • Trong Hieu Tran
    • 1
  1. 1.University of Engineering and TechnologyVietnam National UniversityHanoiVietnam
  2. 2.Wroclaw University of Science and TechnologyWrocławPoland
  3. 3.Nam Dinh University of Technology EducationNam DinhVietnam

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