Skip to main content

On the Properties of Conditional Independence

  • Chapter
Patrick Suppes: Scientific Philosopher

Part of the book series: Synthese Library ((SYLI,volume 234))

Abstract

As the paper explains, it is crucial to epistemology in general and to the theory of causation in particular to investigate the properties of conditional independence as completely as possible. The paper summarizes the most important results concerning conditional independence with respect to two important representations of epistemic states, namely (strictly positive) probability measures and natural conditional (or disbelief or ranking) functions. It finally adds some new observations.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 169.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 219.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

References

  • Carnap, R.: 1950, Logical Foundations of Probability, Chicago University Press, Chicago.

    Google Scholar 

  • Dawid, A. P.: 1979, ‘Conditional Independence in Statistical Theory’, Journal of the Royal Statistical Society B, 41, 1–31.

    Google Scholar 

  • Dawid, A. P.: 1980, ‘Conditional Independence for Statistical Operations’, Annals of Statistics, 8, 598–617.

    Article  Google Scholar 

  • Geiger, D.: 1990, Graphoids: A Qualitative Framework for Probabilistic Inference, Ph.D. Thesis, University of California, Los Angeles.

    Google Scholar 

  • Geiger, D., Paz, A., and Pearl, J.: 1988, ‘Axioms and Algorithms for Inferences Involving Probabilistic Independence’, Technical Report R-119, Cognitive Systems Laboratory, University of California, Los Angeles. Also in: Information and Computation, 91 (1991) 128-141.

    Google Scholar 

  • Geiger, D. and Pearl, J.: 1988, ‘Logical and Algorithmic Properties of Conditional Independence and Qualitative Independence’, Technical Report R-97-IIL, Cognitive Systems Laboratory, University of California, Los Angeles, forthcoming in Annals of Statistics.

    Google Scholar 

  • Geiger, D. and Pearl, J.: 1990, ‘On the Logic of Causal Models’, in: Shachter et al. (1990), pp. 3–14.

    Google Scholar 

  • Geiger, D., Verma, T., and Pearl, J.: 1990, ‘Identifying Independence in Bayesian Networks’, Networks, 20, 507–534.

    Article  Google Scholar 

  • Glymour, C., Spirtes, P., and Schemes, R.: 1991, ‘Causal Inference’, in: W. Spohn (Ed.), Erkenntnis Orientated: A Centennial Volume for Rudolf Carnap and Hans Reichenbach, Kluwer, Dordrecht, pp. 151–189.

    Chapter  Google Scholar 

  • Goldszmidt, M. and Pearl, J.: 1992, ‘Rank-Based Systems: A Simple Approach to Belief Revision, Belief Update, and Reasoning About Evidence and Actions’, in: Proceedings of the Third International Conference on Principles of Knowledge Representation and Reasoning, Cambridge, Ma.

    Google Scholar 

  • Hume, D.: 1739, A Treatise Concerning Human Nature.

    Google Scholar 

  • Hunter, D.: 1991, ‘Graphoids, Semi-Graphoids, and Ordinal Conditional Functions’, International Journal of Approximate Reasoning, 5, 489–504.

    Article  Google Scholar 

  • Lauritzen, S. L., Dawid, A. P., Larsen, B. N., and Leimer, H.-G.: 1990, ‘Independence Properties of Directed Markov Fields’, Networks, 20, 491–505.

    Article  Google Scholar 

  • Matúš, F.: 1988, Independence and Radon Projection on Compact Groups (in Slovak), Ph.D. Thesis, Prague.

    Google Scholar 

  • Mill, J. S.: 1843, System of Logic.

    Google Scholar 

  • Pearl, J.: 1988, Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference, Morgan Kaufman, San Mateo, Ca.

    Google Scholar 

  • Pearl, J. and Paz, A.: 1985, ‘Graphoids: A Graph-Based Logic for Reasoning About Relevance Relations’, Technical Report R-53-L, Cognitive Systems Laboratory, University of California, Los Angeles: also in: B. Du Boulay, D. Hogg, and L. Steels (Eds.), Advances in Artificial Intelligence II, Elsevier, Amsterdam 1987, pp. 357-363.

    Google Scholar 

  • Pearl, J. and Verma, T.: 1991, ‘A Theory of Inferred Causation’, in: J. A. Allen, R. Fikes, and E. Sandewall (Eds.), Principles of Knowledge Representation and Reasoning: Proceedings of the Second International Conference, Morgan Kaufman, San Mateo, Ca., pp. 441–452.

    Google Scholar 

  • Russell, B.: 1912/13, ‘On the Notion of Cause’, Proceedings of the Aristotelian Society, 13, 1–26. Also in: B. Russell, Mysticism and Logic, George Allen & Unwin, London 1963, pp. 132-151.

    Google Scholar 

  • Shachter, R. D., Levitt, T. S., Lemmer, J., and Kanal, L. N. (Eds.): 1990, Uncertainty in Artificial Intelligence 4, Elsevier, Amsterdam.

    Google Scholar 

  • Shenoy, P. P.: 1991, ‘On Spohn’s Rule for Revision of Beliefs’, International Journal of Approximate Reasoning, 5, 149–181.

    Article  Google Scholar 

  • Spirtes, P., Glymour, C., and Scheines, R.: 1993, Causation, Prediction, and Search, Springer, New York.

    Book  Google Scholar 

  • Spohn, W.: 1980, ‘Stochastic Independence, Causal Independence, and Shieldability’, Journal of Philosophical Logic, 9, 73–99.

    Article  Google Scholar 

  • Spohn, W.: 1983, ‘Deterministic and Probabilistic Reasons and Causes’, in: C. G. Hempel, H. Putnam, and W. K. Essler (Eds.), Methodology, Epistemology, and Philosophy of Science. Essays in Honour of Wolfgang Stegmüller on the Occasion of his 60th Birthday, Reidel, Dordrecht, pp. 371–396.

    Google Scholar 

  • Spohn, W.: 1988, ‘Ordinal Conditional Functions. A Dynamic Theory of Epistemic States’, in: W. L. Harper and B. Skyrms (Eds.), Causation in Decision, Belief Change, and Statistics, Vol. II, Kluwer, Dordrecht, pp. 105–134.

    Google Scholar 

  • Spohn, W.: 1990a, ‘A General Non-Probabilistic Theory of Inductive Reasoning’, in: Shachter et al. (1990), pp. 149–158.

    Google Scholar 

  • Spohn, W.: 1990b, ‘Direct and Indirect Causes’, Topoi, 9, 125–145.

    Article  Google Scholar 

  • Spohn, W.: 1991, ‘A Reason for Explanation: Explanations Provide Stable Reasons’, in: W. Spohn, B. C. van Fraassen, and B. Skyrms (Eds.), Existence and Explanation. Essays Presented in Honor of Karel Lambert, Kluwer, Dordrecht, pp. 165–196.

    Google Scholar 

  • Spohn, W.: 1993, ‘Causal Laws are Objectifications of Inductive Schemes’, in: J. Dubucs (Ed.), Philosophy of Probability, Kluwer, Dordrecht, pp. 223–255.

    Google Scholar 

  • Spohn, W.: 1994, ‘On Reichenbach’s Principle of the Common Cause’, in: W. C. Salmon and G. Wolters (Eds.), Logic, Language, and the Structure of Scientific Theories, University of Pittsburgh Press, Pittsburgh, pp. 215–239.

    Google Scholar 

  • Studený, M.: 1989a, ‘Multiinformation and the Problem of Characterization of Conditional Independence Relations’, Problems of Control and Information Theory, 18, 3–16.

    Google Scholar 

  • Studený, M.: 1989b, ‘Attempts at Axiomatic Description of Conditional Independence’, Kybernetika 25, Suppl., 72–80.

    Google Scholar 

  • Studeny, M.: 1992, ‘Conditional Independence Relations Have No Finite Complete Characterization’, in: Transactions of the 1hh Prague Conference on Information Theory, Statistical Decision Functions, Random Processes, Held at Prague 1990, Vol. B, Academia, Prague, pp. 377–396.

    Google Scholar 

  • Studený, M.: 1993, ‘Structural Semigraphoids’, International Journal of General Systems, forthcoming.

    Google Scholar 

  • Suppes, P.: 1970, A Probabilistic Theory of Causality, North-Holland, Amsterdam.

    Google Scholar 

  • Verma, T. and Pearl, J.: 1990, ‘Causal Networks: Semantics and Expressiveness’, in: Shachter et al. (1990), pp. 69–76.

    Google Scholar 

  • Verma, T. and Pearl, J.: 1991, ‘Equivalence and Synthesis of Causal Models’, in: P. P. Bonissone, M. Henrion, L. N. Kanal, and J. F. Lemmer (Eds.), Uncertainty in Artificial Intelligence 6, Elsevier, Amsterdam, pp. 255–268.

    Google Scholar 

References

  • Fine, Terrence: 1973, Theories of Probability, New York, Academic Press.

    Google Scholar 

  • Lehmann, E. L.: 1966, ‘Some Concepts of Dependence’, Annals of Mathematical Statistics, 37, 1137–1153.

    Article  Google Scholar 

  • Suppes, P.: 1970, A Probabilistic Theory of Causality, Amsterdam, North Holland.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1994 Springer Science+Business Media Dordrecht

About this chapter

Cite this chapter

Spohn, W. (1994). On the Properties of Conditional Independence. In: Humphreys, P. (eds) Patrick Suppes: Scientific Philosopher. Synthese Library, vol 234. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-0774-7_7

Download citation

  • DOI: https://doi.org/10.1007/978-94-011-0774-7_7

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-4331-1

  • Online ISBN: 978-94-011-0774-7

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics