Hostname: page-component-586b7cd67f-gb8f7 Total loading time: 0 Render date: 2024-11-25T07:07:16.220Z Has data issue: false hasContentIssue false
  • English
  • Français

FROM CAUSAL MODELS TO COUNTERFACTUAL STRUCTURES

Published online by Cambridge University Press:  12 November 2012

JOSEPH Y. HALPERN
JOSEPH Y. HALPERN*
Affiliation:
Computer Science Department, Cornell University
*
*COMPUTER SCIENCE DEPARTMENT CORNELL UNIVERSITY ITHACA, NY 14853 E-mail: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

Galles & Pearl (l998) claimed that “for recursive models, the causal model framework does not add any restrictions to counterfactuals, beyond those imposed by Lewis’s [possible-worlds] framework.” This claim is examined carefully, with the goal of clarifying the exact relationship between causal models and Lewis’s framework. Recursive models are shown to correspond precisely to a subclass of (possible-world) counterfactual structures. On the other hand, a slight generalization of recursive models, models where all equations have unique solutions, is shown to be incomparable in expressive power to counterfactual structures, despite the fact that the Galles and Pearl arguments should apply to them as well. The problem with the Galles and Pearl argument is identified: an axiom that they viewed as irrelevant, because it involved disjunction (which was not in their language), is not irrelevant at all.

Type
Research Article
Information
The Review of Symbolic Logic , Volume 6 , Issue 2 , June 2013 , pp. 305 - 322
Copyright
Copyright © Association for Symbolic Logic 2012 

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

Bell, J. (1989). The logic of nonmonotonicity. Artificial Intelligence, 41, 365–374.CrossRefGoogle Scholar
Burgess, J. (1981). Quick completeness proofs for some logics of conditionals. Notre Dame Journal of Formal Logic, 22, 76–84.CrossRefGoogle Scholar
Chellas, B. F. (1980). Basic conditional logic. Journal of Philosophical Logic, 4, 133–153.Google Scholar
Friedman, N., & Halpern, J. Y. (1994). On the complexity of conditional logics. In Principles of Knowledge Representation and Reasoning: Proc. Fourth International Conference (KR ’94), Bonn, Germany. pp. 202–213.Google Scholar
Galles, D., & Pearl, J. (1998). An axiomatic characterization of causal counterfactuals. Foundation of Science, 3(1), 151–182.Google Scholar
Grahne, G. (1991). Updates and counterfactuals. In Principles of Knowledge Representation and Reasoning: Proc. Second International Conference (KR ’91), Cambridge, MA. pp. 269–276.Google Scholar
Halpern, J. Y. (2000). Axiomatizing causal reasoning. Journal of Artificial Intelligence Research, 12, 317–337.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.Google Scholar
Katsuno, H., & Satoh, K. (1991). A unified view of consequence relation, belief revision and conditional logic. In Proc. Twelfth International Joint Conference on Artificial Intelligence (IJCAI ’91), Sydney, Australia. pp. 406–412.Google Scholar
Kraus, S., Lehmann, D., & Magidor, M. (1990). Nonmonotonic reasoning, preferential models and cumulative logics. Artificial Intelligence, 44, 167–207.Google Scholar
Lewis, D. (1971). Completeness and decidability of three logics of counterfactual conditionals. Theoria, 37(1), 74–85.Google Scholar
Lewis, D. K. (1973). Counterfactuals. Cambridge, MA: Harvard University Press.Google Scholar
Lewis, D. K. (1974). Intensional logics without iterative axioms. Journal of Philosophical Logic, 3, 457–466.Google Scholar
Pearl, J. (2000). Causality: Models, Reasoning, and Inference. New York: Cambridge University Press.Google Scholar
Stalnaker, R. C. (1968). A theory of conditionals. In Rescher, N., editor. Studies in Logical Theory. Oxford, UK: Blackwell. pp. 98–112.Google Scholar
Zhang, J. (2012). A Lewisian logic of causal counterfactuals. Minds and Machines. To appear. doi: 10.1007/s11023-011-9261-z.Google Scholar
Zhang, J., Lam, W.-Y., & de Clercq, R. (2012). A peculiarity in Pearl’s logic of interventionist counterfactuals. Journal of Philosophical Logic. To appear.Google Scholar