Hostname: page-component-cd9895bd7-mkpzs Total loading time: 0 Render date: 2024-12-26T19:54:40.510Z Has data issue: false hasContentIssue false
  • English
  • Français

APPROPRIATE CAUSAL MODELS AND THE STABILITY OF CAUSATION

Published online by Cambridge University Press:  07 January 2016

JOSEPH Y. HALPERN
JOSEPH Y. HALPERN*
Affiliation:
Cornell University
*
*COMPUTER SCIENCE DEPARTMENT CORNELL UNIVERSITY E-mail: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

Causal models defined in terms of structural equations have proved to be quite a powerful way of representing knowledge regarding causality. However, a number of authors have given examples that seem to show that the Halpern–Pearl (HP) definition of causality (Halpern & Pearl, 2005) gives intuitively unreasonable answers. Here it is shown that, for each of these examples, we can give two stories consistent with the description in the example, such that intuitions regarding causality are quite different for each story. By adding additional variables, we can disambiguate the stories. Moreover, in the resulting causal models, the HP definition of causality gives the intuitively correct answer. It is also shown that, by adding extra variables, a modification to the original HP definition made to deal with an example of Hopkins & Pearl (2003) may not be necessary. Given how much can be done by adding extra variables, there might be a concern that the notion of causality is somewhat unstable. Can adding extra variables in a “conservative” way (i.e., maintaining all the relations between the variables in the original model) cause the answer to the question “Is X = x a cause of Y = y?” to alternate between “yes” and “no”? It is shown that we can have such alternation infinitely often, but if we take normality into consideration, we cannot. Indeed, under appropriate normality assumptions. Adding an extra variable can change the answer from “yes’ to “no”, but after that, it cannot change back to “yes”.

Type
Research Article
Information
The Review of Symbolic Logic , Volume 9 , Issue 1 , March 2016 , pp. 76 - 102
Copyright
Copyright © Association for Symbolic Logic 2016 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

BIBLIOGRAPHY

Aleksandrowicz, G., Chockler, H., Halpern, J. Y., & Ivrii, A. (2014). The computational complexity of structure-based causality. In Brodley, C. E. and Stone, P., editors. Proceedings of Twenty-Eighth National Conference on Artificial Intelligence (AAAI ’14). Palo Alto, California: AAAI Press, pp. 974–980.Google Scholar
Beer, I., Ben-David, S., Chockler, H., Orni, A., & Trefler, R. J. (2012). Explaining counterexamples using causality. Formal Methods in System Design, 40(1), 20–40.CrossRefGoogle Scholar
Blanchard, T., & Schaffer, J. (2013). Cause without default. In Beebee, H., Hitchcock, C., and Price, H., editors. Making a Difference. Oxford: Oxford University Press.Google Scholar
Cushman, F., Knobe, J., & Sinnott-Armstrong, W. (2008). Moral appraisals affect doing/allowing judgments. Cognition, 108(1), 281–289.CrossRefGoogle ScholarPubMed
Eberhardt, F. (2014). Direct causes and the trouble with soft intervention. Erkenntnis, 79(4), 755–777.CrossRefGoogle Scholar
Eiter, T., & Lukasiewicz, T. (2002). Complexity results for structure-based causality. Artificial Intelligence, 142(1), 53–89.CrossRefGoogle Scholar
Gerstenberg, T., & Lagnado, D. (2010). Spreading the blame: The allocation of responsibility amongst multiple agents. Cognition, 115, 166–171.CrossRefGoogle ScholarPubMed
Glymour, C., Danks, D., Glymour, B., Eberhardt, F., Ramsey, J., Scheines, R., Spirtes, P., Teng, C. M., & Zhang, J. (2010). Actual causation: A stone soup essay. Synthese, 175, 169–192.CrossRefGoogle Scholar
Hall, N. (2007). Structural equations and causation. Philosophical Studies, 132, 109–136.CrossRefGoogle Scholar
Halpern, J. Y. (2008). Defaults and normality in causal structures. In Brewka, G. and Lang, J., editors. Principles of Knowledge Representation and Reasoning: Proceedings of the Eleventh International Conference (KR ’08). Palo Alto, California: AAAI Press, pp. 198–208.Google Scholar
Halpern, J. Y., & Hitchcock, C. (2010). Actual causation and the art of modeling. In Dechter, R., Geffner, H., and Halpern, J., editors. Causality, Probability, and Heuristics: A Tribute to Judea Pearl, pp. 383–406. London: College Publications.Google Scholar
Halpern, J. Y., & Hitchcock, C. (2015). Graded causation and defaults. British Journal for the Philosophy of Science, 66(2), 413–457.CrossRefGoogle Scholar
Halpern, J. Y., & Pearl, J. (2001). Causes and explanations: A structural-model approach. Part I: Causes. In Breese, J. S. and Koller, D., editors. Proceedings of the Seventeenth Conference on Uncertainty in Artificial Intelligence (UAI 2001). San Francisco, California: Morgan Kaufmann, pp. 194–202.Google Scholar
Halpern, J. Y., & Pearl, J. (2005). Causes and explanations: A structural-model approach. Part I: Causes. British Journal for Philosophy of Science, 56(4), 843–887.CrossRefGoogle Scholar
Hiddleston, E. (2005). Causal powers. British Journal for Philosophy of Science, 56, 27–59.CrossRefGoogle Scholar
Hitchcock, C. (2001). The intransitivity of causation revealed in equations and graphs. Journal of Philosophy, XCVIII(6), 273–299.CrossRefGoogle Scholar
Hitchcock, C. (2007). Prevention, preemption, and the principle of sufficient reason. Philosophical Review, 116, 495–532.CrossRefGoogle Scholar
Hitchcock, C., & Knobe, J. (2009). Cause and norm. Journal of Philosophy, 106, 587–612.CrossRefGoogle Scholar
Hopkins, M. (2001). A proof of the conjunctive cause conjecture. Unpublished manuscript.Google Scholar
Hopkins, M., & Pearl, J. (2003). Clarifying the usage of structural models for commonsense causal reasoning. In Doherty, P., McCarthy, J., and Williams, M-A., editors. Proceedings of the AAAI Spring Symposium on Logical Formalization of Commonsense Reasoning. Palo Alto, California: AAAI Press.Google Scholar
Kahneman, D., & Miller, D. T. (1986). Norm theory: Comparing reality to its alternatives. Psychological Review, 94(2), 136–153.CrossRefGoogle Scholar
Knobe, J., & Fraser, B. (2008). Causal judgment and moral judgment: Two experiments. In Sinnott-Armstrong, W., editor. Moral Psychology: The Cognitive Science of Morality, Vol. 2, pp. 441–447. Cambridge, MA: MIT Press.Google Scholar
Lagnado, D. A., Gerstenberg, T., & Zultan, R. (2013). Causal responsibility and counterfactuals. Cognitive Science, 37, 1036–1073.CrossRefGoogle ScholarPubMed
Livengood, J. (2013). Actual causation in simple voting scenarios. Nous, 47(2), 316–345.CrossRefGoogle Scholar
Spohn, W. (2008). Personal email.Google Scholar
Strevens, M. (2008). Comments on woodward, making things happen. Philosophy and Phenomenology, 77(1), 171–192.CrossRefGoogle Scholar
Weslake, B. (2015). A partial theory of actual causation. British Journal for the Philosophy of Science. To appear.Google Scholar
Woodward, J. (2003). Making Things Happen: A Theory of Causal Explanation. Oxford, U.K.: Oxford University Press.Google Scholar