Studia Logica

, Volume 102, Issue 4, pp 751–769 | Cite as

Structural Inference from Conditional Knowledge Bases

Article

Abstract

There are several approaches implementing reasoning based on conditional knowledge bases, one of the most popular being System Z (Pearl, Proceedings of the 3rd conference on theoretical aspects of reasoning about knowledge, TARK ’90, Morgan Kaufmann Publishers Inc., San Francisco, CA, USA, pp. 121–135, 1990). We look at ranking functions (Spohn, The Laws of Belief: Ranking Theory and Its Philosophical Applications, Oxford University Press, Oxford, 2012) in general, conditional structures and c-representations (Kern-Isberner, Conditionals in Nonmonotonic Reasoning and Belief Revision: Considering Conditionals as Agents, vol. 2087 of LNCS, Springer, Berlin, 2001) in order to examine the reasoning strength of the different approaches by learning which of the known calculi of nonmonotonic reasoning (System P and R) and Direct Inference are applicable to these inference relations. Furthermore we use the recently proposed Enforcement-postulate (Kern-Isberner and Krümpelmann, Proceedings of the 22nd international joint conference on artificial intelligence, vol. 2, IJCAI’11, AAAI Press, pp. 937–942, 2011) to show dependencies between these approaches.

Keywords

Conditionals Ranking functions C-representations System P System R System Z 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Adams, E. W., The Logic of Conditionals, D. Reidel, Dordrecht, 1975.Google Scholar
  2. 2.
    Arló-Costa H., R. Parikh.: Conditional probability and defeasible inference. Journal of Philosophical Logic. 34(1), 97–113 (2005)CrossRefGoogle Scholar
  3. 3.
    Benferhat, S., J. Bonnefon, and R. Neves, An overview of possibilistic handling of default reasoning, with experimental studies, Synthese 146:53–70, 2005.Google Scholar
  4. 4.
    Benferhat, S., C. Cayrol, D. Dubois, J. Lang, and H. Prade, Inconsistency management and prioritized syntax-based entailment, in Proceedings of the International Joint Conferences on Artificial Intelligence, 1993, pp. 640–647.Google Scholar
  5. 5.
    De Finetti, B., Theory of Probability, vols. 1, 2, John Wiley & Sons, NY, USA, 1974.Google Scholar
  6. 6.
    Dubois, D., and H. Prade, Conditional objects as non-monotonic consequence relationships, IEEE Transaction on Systems, Man, and Cybernetics 24(12):1724–1740, 1994.Google Scholar
  7. 7.
    Gilio, A., and G. Sanfilippo, Conditional random quantities and compounds of conditionals, Studia Logica 102, 2014.Google Scholar
  8. 8.
    Goldszmidt M., J. Pearl: Qualitative probabilities for default reasoning. belief revision, and causal modeling. Artificial Intelligence 84(1–2), 57–112 (1996)Google Scholar
  9. 9.
    Kern-Isberner, G., A structural approach to default reasoning, in Proceedings of the Eighth International Conference on Principles of Knowledge Representation and Reasoning, KR’2002, Morgan Kaufmann, San Francisco, CA, 2002, pp. 147–157.Google Scholar
  10. 10.
    Kern-Isberner, G., Conditionals in Nonmonotonic Reasoning and Belief Revision: Considering Conditionals as Agents, vol. 2087 of LNCS, Springer, Berlin, 2001.Google Scholar
  11. 11.
    Kern-Isberner, G., and P. Krümpelmann, A constructive approach to independent and evidence retaining belief revision by general information sets, in Proceedings of the 22nd international joint conference on Artificial Intelligence, vol. 2, IJCAI’11, AAAI Press, 2011, pp. 937–942.Google Scholar
  12. 12.
    Kraus, S., D. Lehmann, and M. Magidor, Nonmonotonic reasoning, preferential models and cumulative logics, Artificial Intelligence Journal 44(167):167–207, 1990.Google Scholar
  13. 13.
    Lukasiewicz T.: Weak nonmonotonic probabilistic logics. Artificial Intelligence. 168(1–2), 119–161 (2005)CrossRefGoogle Scholar
  14. 14.
    Makinson, D., General patterns in nonmonotonic reasoning, in D. M. Gabbay, C. J. Hogger, and J. A. Robinson (eds.), Handbook of Logic in Artificial Intelligence and Logic Programming, vol. 3, Oxford University Press, Inc., New York, NY, USA, 1994, pp. 35–110.Google Scholar
  15. 15.
    Pearl, J., Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference, Morgan Kaufmann Publishers Inc., San Francisco, CA, USA, 1988.Google Scholar
  16. 16.
    Pearl, J., System Z: A natural ordering of defaults with tractable applications to nonmonotonic reasoning, in Proceedings of the 3rd conference on Theoretical aspects of reasoning about knowledge (TARK ’90). Morgan Kaufmann Publishers Inc., San Francisco, CA, USA, 1990, pp. 121–135.Google Scholar
  17. 17.
    Pfeifer, N., Reasoning about uncertain conditionals, Studia Logica 102, 2014.Google Scholar
  18. 18.
    Pfeifer N., Kleiter G. D: Coherence and nonmonotonicity in human reasoning. Synthese. 146(1–2), 93–109 (2005)CrossRefGoogle Scholar
  19. 19.
    Spohn W.: The Laws of Belief: Ranking Theory and Its Philosophical Applications. Oxford University Press, Oxford (2012)CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  1. 1.Chair 1 Computer Science—Information EngineeringTechnische Universität DortmundDortmundGermany

Personalised recommendations