Formal properties of conditional independence in different calculi of AI

  • Milan Studený
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 747)


In this paper formal properties of CI in different frameworks are studied. The first part is devoted to the comparison of three different frameworks for study CI: probability theory, theory of relational databases and Spohn's theory of ordinal conditional functions. Although CI-models arising in these frameworks are very similar (they satisfy semigraphoid axioms) we give examples showing that their formal properties still differ (each other). On the other hand, we find that (within each of these frameworks) there exists no finite complete axiomatic characterization of CI-models by finding an infinite set of sound inference rules (the same in all three frameworks). In the second part further frameworks for CI are discussed: Dempster-Shafer theory, possibility theory and (general) Shenoy's theory of valuation-based systems.


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  1. 1.
    L.M. de Campos, J.F. Huete: Independence concepts in upper and lower probabilities. In: Proceedings of IPMU'92 (inter. conf. on Information Processing and Management of Uncertainty in knowledge-based systems, Mallorca, July 6–10, 1992), 129–132Google Scholar
  2. 2.
    A.P. Dawid: Conditional independence in statistical theory. Journal of the Royal Statistical Society B 41, 1–31 (1979)Google Scholar
  3. 3.
    M. Goldszmidt, J. Pearl: Rank-based systems: a simple approach to belief revision, belief update, and reasoning about evidence and actions. In: Proceedings of the 3rd International Conference on Principles of Knowledge Representation and Reasoning, Cambridge, MA, October 1992, 661–672Google Scholar
  4. 4.
    D. Hunter: Graphoids and natural conditional functions. International Journal of Approximate Reasoning 5, 489–504 (1991)Google Scholar
  5. 5.
    G.J. Klir, T.A.Folger: Fuzzy Sets, Uncertainty and Information. Prentice Hall. Englewood Cliffs, N.J. 1988Google Scholar
  6. 6.
    J. Pearl: Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference. Morgan Kaufman. San Máteo, California 1988Google Scholar
  7. 7.
    Y. Sagiv, S.F. Walecka: Subset dependencies and completeness result for a subclass of embedded multivalued dependencies. Journal of the Association for Computing Machinery 29, 103–117 (1982)Google Scholar
  8. 8.
    G. Shafer, P.P. Shenoy, K. Mellouli: Propagating belief functions in qualitative Markov trees. International Journal of Approximate Reasoning 1, 349–400 (1987)Google Scholar
  9. 9.
    P.P. Shenoy: On Spohn's rule for revision of beliefs. International Journal of Approximate Reasoning 5, 149–181 (1991)Google Scholar
  10. 10.
    P.P. Shenoy: Conditional independence in valuation-based systems. School of Business working paper n. 236, University of Kansas, Lawrence 1992, submitted to Annals of StatisticsGoogle Scholar
  11. 11.
    W. Spohn: Stochastic independence, causal independence and shieldability. Journal of Philosophical Logic 9, 73–99 (1980)Google Scholar
  12. 12.
    W. Spohn: Ordinal conditional functions: a dynamic theory of epistemic states. In: W.L. Harper, B. Skyrms (eds.): Causation in Decision, Belief Change, and Statistics, vol. II. Kluwer Academic Publishers. Dordrecht 1988, 105–134Google Scholar
  13. 13.
    W. Spohn: On the properties of conditional independence, to appear in P. Humphreys (eds.): Patrick Suppes — Mathematical Philosopher. Synthese 1993Google Scholar
  14. 14.
    M. Studený: Multiinformation and the problem of characterization of conditional independence relations. Problems of Control and Information Theory 18, 3–16 (1989)Google Scholar
  15. 15.
    M.Studený: Conditional independence relations have no finite complete characterization. In: Transactions of 11-th Prague Conference on Information Theory, Statistical Decision Functions and Random Processes vol.B. Academia. Prague 1992, 377–396Google Scholar
  16. 16.
    M. Studený: Conditional independence and natural conditional functions, submitted to International Journal of Approximate ReasoningGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1993

Authors and Affiliations

  • Milan Studený
    • 1
  1. 1.Institute of Information Theory and AutomationAcademy of Sciences of Czech RepublicPrague 8Czech Republic

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