Extending and Formalizing Bayesian Networks by Strong Relevant Logic

  • Jianzhe Zhao
  • Ying Liu
  • Jingde Cheng
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7802)

Abstract

In orders to deal with uncertainty by systematical methodologies, some structural models combining probability theory with logic systems have been proposed. However, these models used only the formal language part of the underlying logic system to represent empirical knowledge of target domains, but not asked the logical consequence theory part of the underlying logic system to reason about empirical theorems that are logically implied in domain knowledge. As the first step to establish a unifying framework to support uncertainty reasoning, this paper proposes a new framework that extends and formalizes traditional Bayesian networks by combining Bayesian networks with strong relevant logic. The most intrinsic feature of the framework is that it provides a formal system for representing and reasoning about generalized Bayesian networks, and therefore, within the framework, for given empirical knowledge in a specific target domain, one can reason out those new empirical theorems that are certainly relevant to given empirical knowledge. As a result, using an automated forward reasoning engine based on strong relevant logic, it is possible to get Bayesian networks semi-automatically.

Keywords

Uncertainty reasoning Bayesian networks Strong relevant logic Forward reasoning Free-EnCal 

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References

  1. 1.
    Pearl, J.: Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference. Morgan Kaufmann (1988)Google Scholar
  2. 2.
    Pearl, J.: Causality: Models, Reasoning, and Inference, 2nd edn. Cambridge University Press (2009)Google Scholar
  3. 3.
    Haenni, R., Romeijn, J.W., Wheeler, G., Williamson, J.: Probabilistic Logics and Probabilistic Networks. Springer (2010)Google Scholar
  4. 4.
    Fierens, D., Blockeel, H., Bruynooghe, M., Ramon, J.: Logical Bayesian Networks and Their Relation to other Probabilistic Logical Models. In: Kramer, S., Pfahringer, B. (eds.) ILP 2005. LNCS (LNAI), vol. 3625, pp. 121–135. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  5. 5.
    Kersting, K., Raedt, L.D.: Bayesian Logic Programs. Technical Report 151, Institute for Computer Science, University of Freiburg, Germany (2001)Google Scholar
  6. 6.
    Fierens, D., Blockeel, H., Bruynooghe, M., Ramon, J.: Logical Bayesian Networks. In: Proceedings of the 3rd Workshop on Multi-Relational Data Mining (MRDM 2004), pp. 19–30 (2004)Google Scholar
  7. 7.
    Cheng, J.: A Strong Relevant Logic Model of Epistemic Processes in Scientific Discovery. In: Information Modeling and Knowledge Bases XI. Frontiers in Artificial Intelligence and Applications, vol. 61, pp. 136–159. IOS Press (2000)Google Scholar
  8. 8.
    Cheng, J.: Strong Relevant Logic as the Universal Basis of Various Applied Logics for Knowledge Representation and Reasoning. In: Information Modeling and Knowledge Bases XVII. Frontiers in Artificial Intelligence and Applications, vol. 136, pp. 310–320. IOS Press (2006)Google Scholar
  9. 9.
    Anderson, A.R., Belnap Jr., N.D.: Entailment: The Logic of Relevance and Necessity, vol. I. Princeton University Press (1975)Google Scholar
  10. 10.
    Anderson, A.R., Belnap Jr., N.D., Dunn, J.M.: Entailment: The Logic of Relevance and Necessity, vol. II. Princeton University Press (1992)Google Scholar
  11. 11.
    Dunn, J.M., Restall, G.: Relevance Logic. In: Gabbay, D., Guenthner, F. (eds.) Handbook of Philosophical Logic, 2nd edn., vol. 6, pp. 1–128. Kluwer Academic (2002)Google Scholar
  12. 12.
    Mares, E.D.: Relevant Logic: A Philosophical Interpretation. Cambridge University Press (2004)Google Scholar
  13. 13.
    Cheng, J., Nara, S., Goto, Y.: FreeEnCal: A Forward Reasoning Engine with General-Purpose. In: Apolloni, B., Howlett, R.J., Jain, L. (eds.) KES 2007, Part II. LNCS (LNAI), vol. 4693, pp. 444–452. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  14. 14.
    Poole, D.: The Independent Choice Logic for modeling multiple agents under uncertainty. Artificial Intelligence 94(1-2), 5–56 (1997)MathSciNetCrossRefGoogle Scholar
  15. 15.
    Sato, T., Kameya, Y.: PRISM: A symbolic-statistical modeling language. In: Proceeding of the 15th International Joint Conference on Artificial Intelligence (IJCAI 1997), pp. 1330–1335 (1997)Google Scholar
  16. 16.
    Cussens, J.: Parameter estimation in stochastic logic programs. Machine Learning 44(3), 245–271 (2001)MATHCrossRefGoogle Scholar
  17. 17.
    Borgelt, C., Gebhardt, J., Kruse, R.: Graphical models. In: Proceedings of International School for the Synthesis of Expert Knowledge, Citeseer (2002)Google Scholar
  18. 18.
    Friedman, N., Getoor, L., Koller, D., Pfeffer, A.: Learning probabilistic relational models. In: Proceedings of the 16th International Joint Conference on Artificial Intelligence (IJCAI 1999), pp. 1300–1309 (1999)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Jianzhe Zhao
    • 1
    • 2
  • Ying Liu
    • 2
  • Jingde Cheng
    • 3
  1. 1.School of Business AdministrationNortheastern UniversityShenyangP.R. China
  2. 2.Software CollegeNortheastern UniversityShenyangP.R. China
  3. 3.Department of Information and Computer SciencesSaitama UniversitySaitamaJapan

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