Statistics and Computing

, Volume 2, Issue 2, pp 91–95 | Cite as

A statistical semantics for causation

  • Judea Pearl
  • Thomas S. Verma


We propose a model-theoretic definition of causation, and show that, contrary to common folklore, genuine causal influences can be distinguished from spurious covariations following standard norms of inductive reasoning. We also establish a sound characterization of the conditions under which such a distinction is possible. Finally, we provide a proof-theoretical procedure for inductive causation and show that, for a large class of data and structures, effective algorithms exist that uncover the direction of causal influences as defined above.


Causality induction learning 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Cartwright, N. (1989)Nature Capacities and Their Measurements Clarendon Press, Oxford.Google Scholar
  2. Cliff, N. (1983) Some cautions concerning the application of causal modeling methods.Multivariate Behavioral Research,18, 115–126.Google Scholar
  3. Freedman (1987) As others see us: a case study in path analysis (with discussion).Journal of Educational Statistics,12, 101–223.Google Scholar
  4. Gardenfors, P. (1988) Causation and the dynamics of belief, inCausation in Decision, Belief Change and Statistics II, Harper, W. L. and Skyrms, B. (eds), Kluwer Academic Publishers, Dordrecth, pp. 85–104.Google Scholar
  5. Glymour, C., Scheines, R., Spirtes, P. and Kelly, K. (1987)Discovering Causal Structure, Academic Press, New York.Google Scholar
  6. Granger, C. W. J. (1988) Causality testing in a decision science, inCausation in Decision, Belief Change and Statistics I, Harper, W. L. and Skyrms, B. (eds), Kluwer Academic Publishers, Dordrecht, pp. 1–20.Google Scholar
  7. Holland, P. (1986) Statistics and causal inference.Journal of the American Statistical Association,81, 945–960.Google Scholar
  8. Kautz, H. (1987) A formal theory of plan recognition. PhD thesis, University of Rochester, Rochester, NY.Google Scholar
  9. Otte, R. (1981) A critique of Suppes' theory of probabilistic causality.Synthese,48, 167–189.Google Scholar
  10. Pearl, J. (1988)Probabilistic Reasoning in Intelligent Systems, Morgan Kaufmann, San Mateo, CA.Google Scholar
  11. Pearl, J. (1990) Probabilistic and qualitative abduction, inProceedings of AAAI Spring Symposium on Abduction, Stanford, March 27–29, pp. 155–158.Google Scholar
  12. Pearl, J. and Verma, T. S. (1987) The logic of representing dependencies by directed acyclic graphs.Proceedings of AAAI-87, Seattle, Washington, pp. 347–379.Google Scholar
  13. Pearl, J. and Verma, T. S. (1991) A theory of inferred causation. In Allen J. A., Fikes, R. and Sandwall, E. (eds),Principles of Knowledge Representation and Reasoning: Proceedings of the Second International Conference, pp. 441–452. Morgan Kaufmann, San Mateo.Google Scholar
  14. Reichenbach, H. (1956)The Direction of Time, University of California Press, Berkeley.Google Scholar
  15. Simon, H. (1954) Spurious correlations: a causal intepretation.Journal American Statistical Association,49, 469–492.Google Scholar
  16. Spirtes, P. and Glymour, C. (1991) An algorithm for fast recovery of sparse causal graphs.Social Science Computer Review,9, 62–72.Google Scholar
  17. Spirtes, P., Glymour, C. and Scheines, R. (1989) Causality from probability. Technical Report CMU-LCL-89-4, Department of Philosophy, Carnegie-Mellon University.Google Scholar
  18. Spohn, W. (1983) Deterministic and probabilistic reasons and causes.Erkenntnis,19, 371–396.Google Scholar
  19. Suppes, P. (1970)A Probabilistic Theory of Causation, North-Holland, Amsterdam.Google Scholar
  20. Verma, T. S. and Pearl, J. (1990) Equivalence and synthesis of causal models, inProceedings of the 6th Conference on Uncertainty in Artificial Intelligence, Cambridge, MA, pp. 220–227. Also published, North-Holland, Amsterdam (1991) 255–268.Google Scholar
  21. Verma, T. S. (1992) Invariant properties of causal models.Technical Report R-134, UCLA Cognitive Systems Laboratory.Google Scholar

Copyright information

© Chapman & Hall 1992

Authors and Affiliations

  • Judea Pearl
    • 1
  • Thomas S. Verma
    • 1
  1. 1.Cognitive Systems Laboratory, Computer Science DepartmentUniversity of CaliforniaLos AngelesUSA

Personalised recommendations