Advertisement

Minds and Machines

, Volume 23, Issue 1, pp 77–93 | Cite as

A Lewisian Logic of Causal Counterfactuals

  • Jiji Zhang
Article

Abstract

In the artificial intelligence literature a promising approach to counterfactual reasoning is to interpret counterfactual conditionals based on causal models. Different logics of such causal counterfactuals have been developed with respect to different classes of causal models. In this paper I characterize the class of causal models that are Lewisian in the sense that they validate the principles in Lewis’s well-known logic of counterfactuals. I then develop a system sound and complete with respect to this class. The resulting logic is the weakest logic of causal counterfactuals that respects Lewis’s principles, sits in between the logic developed by Galles and Pearl and the logic developed by Halpern, and stands to Galles and Pearl’s logic in the same fashion as Lewis’s stands to Stalnaker’s.

Keywords

Causal models Causal reasoning Conditional logic Counterfactual Intervention 

Notes

Acknowledgments

I thank Lam Wai Yin for helpful discussions on issues related to this article, and the audiences of a seminar at Carnegie Mellon University for useful feedback. My research was supported in part by the Research Grants Council of Hong Kong under the General Research Fund LU341910.

References

  1. Ellis, B., Jackson, F., & Pargetter, R. (1977). An objection to possible-world semantics for counterfactual logics. Journal of Philosophical Logic, 6, 355–357.MathSciNetMATHCrossRefGoogle Scholar
  2. Fisher, F. M. (1970). A correspondence principle for simultaneous equation models. Econometrica, 38, 73–92.CrossRefGoogle Scholar
  3. Galles, D., & Pearl, J. (1998). An axiomatic characterization of causal counterfactuals. Foundation of Science, 3, 151–182.MathSciNetCrossRefGoogle Scholar
  4. Ginsberg, M. L. (1986). Counterfactuals. Artificial Intelligence, 30, 35–79.MathSciNetMATHCrossRefGoogle Scholar
  5. Ginsberg, M. L., & Smith, D. E. (1987). Reasoning about action I: A possible worlds approach. In F. M. Brown (Ed.), The frame problem in artificial intelligence (pp. 233–258). Los Altos, CA: Morgan Kaufmann.Google Scholar
  6. Halpern, J. Y. (2000). Axiomatizing causal reasoning. Journal of Artificial Intelligence Research, 12, 317–337.MathSciNetMATHGoogle Scholar
  7. Harel, D. (1979). First-order dynamic logic. Berlin & New York: Springer.MATHCrossRefGoogle Scholar
  8. Hiddleston, E. (2005). A causal theory of counterfactuals. Noûs, 39, 632–657.MathSciNetCrossRefGoogle Scholar
  9. Hughes, G. E., & Cresswell, M. J. (1996). A new introduction to modal logic. London & New York: Routledge.MATHCrossRefGoogle Scholar
  10. Lewis, D. (1973). Counterfactuals. Oxford: Blackwell.Google Scholar
  11. Lewis, D. (1977). Possible-world semantics for counterfactual logics: A rejoinder. Journal of Philosophical Logic, 6, 359–363.MathSciNetMATHCrossRefGoogle Scholar
  12. Pearl, J. (1995). Causal diagrams for empirical research. Biometrika, 82, 669–710.MathSciNetMATHCrossRefGoogle Scholar
  13. Pearl, J. (1998). Graphs, causality, and structural equation models. Sociological Methods and Research, 27, 226–284.CrossRefGoogle Scholar
  14. Pearl, J. (2009). Causality: Models, reasoning, and inference (2nd ed.). Cambridge, UK: Cambridge University Press.MATHGoogle Scholar
  15. Spirtes, P., Glymour, G., & Scheines, R. (2000). Causation, prediction, and search (2nd ed.). Cambridge, MA: MIT Press.Google Scholar
  16. Stalnaker, R. (1968). A theory of conditionals. In N. Rescher (Ed.), Studies in logical theory (pp. 98–112). Oxford: Blackwell.Google Scholar
  17. Stalnaker, R., & Thomason, R. H. (1970). A semantic analysis of conditional logic. Theoria, 36, 23–42.MATHCrossRefGoogle Scholar
  18. Strotz, R. H., & Wold, H. O. A. (1960). Recursive versus nonrecursive systems: An attempt at synthesis. Econometrica, 28, 417–427.MathSciNetCrossRefGoogle Scholar
  19. Winslett, M. (1988). Reasoning about action using a possible worlds approach. In Proceedings of the Seventh American Association of Artificial Intelligence Conference (pp. 89–93).Google Scholar
  20. Woodward, J. (2003). Making things happen: A theory of causal explanation. Oxford & New York: Oxford University Press.Google Scholar
  21. Woodward, J., & Hitchcock, C. (2003). Explanatory generalizations, part I: A counterfactual account. Noûs, 37, 1–24.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  1. 1.Department of PhilosophyLingnan UniversityTuen MunHong Kong

Personalised recommendations