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Qualitative and quantitative conditions for the transitivity of perceived causation:

Theoretical and experimental results

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Abstract

If A caused B and B caused C, did A cause C? Although laypersons commonly perceive causality as being transitive, some philosophers have questioned this assumption, and models of causality in artificial intelligence are often agnostic with respect to transitivity. We consider two formal models of causation that differ in the way they represent uncertainty. The quantitative model uses a crude probabilistic definition, arguably the common core of more sophisticated quantitative definitions; the qualitative model uses a definition based on nonmonotonic consequence relations. Different sufficient conditions for the transitivity of causation are laid bare by the two models: The Markov condition on events for the quantitative model, and a so-called saliency condition (A is perceived as a typical cause of B) for the qualitative model. We explore the formal and empirical relations between these sufficient conditions, and between the underlying definitions of perceived causation. These connections shed light on the range of applicability of each model, contrasting commonsense causal reasoning (supposedly qualitative) and scientific causation (more naturally quantitative). These speculations are supported by a series of three behavioral experiments.

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References

  1. Adams, E.: The Logic of Conditionals: An Application of Probability to Deductive Logic. Reidel, Dordrecht (1975)

    MATH  Google Scholar 

  2. Barbey, A.K., Wolff, P.: Causal reasoning from forces. In: Sun, R., Miyake, N. (eds.) Proceedings of the 28th Annual Conference of the Cognitive Science Society, p. 2439. Erlbaum, Mahwah (2006)

    Google Scholar 

  3. Barbey, A.K., Wolff, P.: Learning causal structure from reasoning. In: McNamara, D.S., Trafton, J.G. (eds.) Proceedings of the 29th Annual Conference of the Cognitive Science Society, pp. 713–718. Cognitive Science Society, Austin (2007)

    Google Scholar 

  4. Bell, J.: Causation as production. In: Brewka, G., Coradeschi, S., Perini, A., Traverso, P. (eds.) Proceedings of the 17th European Conference on Artificial Intelligence (ECAI’06), pp. 327–331 (2006)

  5. Benferhat, S., Bonnefon, J.F., Chassy, P., Da Silva Neves, R.M., Dubois, D., Dupin de Saint-Cyr, F., Kayser, D., Nouioua, F., Nouioua-Boutouhami, S., Prade, H., Smaoui, S.: A comparative study of six formal models of causal ascription. Lect. Notes Artif. Intell. 5291, 47–62 (2008)

    Google Scholar 

  6. Benferhat, S., Bonnefon, J.F., Da Silva Neves, R.M.: An overview of possibilistic handling of default reasoning, with experimental studies. Synthese 146, 53–70 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  7. Benferhat, S., Dubois, D., Prade, H.: Nonmonotonic reasoning, conditional objects and possibility theory. Artif. Intell. 92, 259–276 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  8. Benferhat, S., Dubois, D., Prade, H.: Possibilistic and standard probabilistic semantics of conditional knowledge bases. J. Logic Comput. 9, 873–895 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  9. Bjornsson, G.: How effects depend on their causes,why causal transitivity fails, and why we care about causation. Philos. Stud. 133, 349–390 (2007)

    Article  MathSciNet  Google Scholar 

  10. Bonnefon, J.F., Da Silva Neves, R.M., Dubois, D., Prade, H.; Background default knowledge and causality ascriptions. In: Brewka, G., Coradeschi, S., Perini, A., Traverso, P. (eds.) Proceedings of the 17th European Conference on Artificial Intelligence (ECAI’06), pp. 11–15. IOS Press, Zurich (2006)

    Google Scholar 

  11. Bonnefon, J.F., Da Silva Neves, R.M., Dubois, D., Prade, H.: Predicting causality ascriptions from background knowledge: model and experimental validation. Internat. J. Approx. Reason. 48, 752–765 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  12. Bonnefon, J.F., Dubois, D., Prade, H.: Transitive observation-based causation, saliency, and the Markov condition. Lect. Notes Artif. Intell. 5291, 78–91 (2008)

    Google Scholar 

  13. Buehner, M., Cheng, P.W., Clifford, D.: From covariation to causation: a test of the assumption of causal power. J. Exp. Psychol. Learn. 29, 1119–1140 (2003)

    Article  Google Scholar 

  14. Campion, N.: Hypothetical and certain inferences from conditional arguments read in text. J. Exp. Psychol. Learn. 32, 547–558 (2006)

    Article  Google Scholar 

  15. Cheng, P.W.: From covariation to causation: a causal power theory. Psychol. Rev. 104, 367–405 (1997)

    Article  Google Scholar 

  16. Cheng, P.W., Novick, L.R.: Causes versus enabling conditions. Cognition 40, 83–120 (1991)

    Article  Google Scholar 

  17. Cheng, P.W., Novick, L.R.: Covariation in natural causal induction. Psychol. Rev. 99, 365–382 (1992)

    Article  Google Scholar 

  18. Da Silva Neves, R.M., Bonnefon, J.F., Raufaste, E.: An empirical test for patterns of nonmonotonic inference. Ann. Math. Artif. Intell. 34, 107–130 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  19. De Neys, W., Schaeken, W., d’Ydewalle, G.: Causal conditional reasoning and semantic memory retrieval: a test of the semantic memory framework. Mem. Cognition 30, 908–920 (2002)

    Article  Google Scholar 

  20. Dubois, D., Fargier, H., Prade, H.: Ordinal and probabilistic representations of acceptance. J. Artif. Intell. Res. 22, 23–56 (2004)

    MathSciNet  MATH  Google Scholar 

  21. Dubois, D., Fariñas Del Cerro, L., Herzig, A., Prade, H.: A roadmap of qualitative independence. In D. Dubois, Prade, H., Klement, E.P. (eds.) Fuzzy Sets, Logics and Reasoning about Knowledge, Applied Logic, vol. 15, pp. 325–350. Kluwer, Dordrecht (1999)

    Google Scholar 

  22. Dubois, D., Godo, L., Lopez de Mantaras, R., Prade, H.: Qualitative reasoning with imprecise probabilities. J. Intell. Inform. Syst. 2, 319–363 (1993)

    Article  Google Scholar 

  23. Dubois, D., Prade, H.: Semantic considerations on order of magnitude reasoning. In: Singh, M.G., Travé-Massuyès, L. (eds.) Decision Support Systems and Qualitative Reasoning, pp. 223–228. North-Holland (1991)

  24. Dubois, D., Prade, H.: Conditional objects as nonmonotonic consequence relations: main results. In: Doyle, J., Sandewall, E., Torasso, P. (eds.) KR’94: Principles of Knowledge Representation and Reasoning, pp. 170–177. Morgan Kaufmann, San Francisco (1994)

    Google Scholar 

  25. Dubois, D., Prade, H.: Modeling the role of (ab)normality in the ascription of causality judgements by agents. In: Morgenstern, L., Pagnucco, M. (eds.) Proceedings of IJCAI-05 Workshop on Nonmonotonic Reasoning, Action, and Change (NRAC05), pp. 22–27. Edinburg, Scotland (2005)

    Google Scholar 

  26. Eells, E., Sober, E.: Probabilistic causality and the question of transitivity. Philos. Sci. 50, 35–57 (1983)

    Article  MathSciNet  Google Scholar 

  27. Gilio, A.: Probabilistic reasoning under coherence in system P. Ann. Math. Artif. Intell. 34, 5–34 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  28. Goldvarg, E., Johnson-Laird, P.N.: Naive causality: a mental model theory of causal meaning and reasoning. Cognitive Sci. 25, 565–610 (2001)

    Article  Google Scholar 

  29. Good, I.J.: A causal calculus I. British J. Philos. Sci 11, 305–318 (1961)

    Article  MathSciNet  Google Scholar 

  30. Good, I.J.: A causal calculus II. British J. Philos. Sci. 12, 43–51 (1962)

    MathSciNet  Google Scholar 

  31. Hall, N.: Causation and the price of transitivity. J. Philos. 97, 198–222 (2000)

    Article  Google Scholar 

  32. Halpern, J., Pearl, J.: Causes and explanations: a structural-model approach—part 1: Causes. British J. Philos. Sci. 56, 843–887 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  33. Hesslow, G.: The transitivity of causation. Analysis 41, 130–133 (1981)

    Article  Google Scholar 

  34. Hitchcock, C.: The intransitivity of causation revealed in equations and graphs. J. Philos. 98, 273–299 (2001)

    Article  MathSciNet  Google Scholar 

  35. Kraus, S., Lehmann, D., Magidor, M.: Nonmonotonic reasoning, preferential models and cumulative logics. Artif. Intell. 44, 167–207 (1990)

    Article  MathSciNet  MATH  Google Scholar 

  36. Kvart, I.: Transitivity and preemption of causal relevance. Philos. Stud. 64, 125–160 (1991)

    Article  Google Scholar 

  37. Kyburg, H.E.: Probability and the Logic of Rational Belief. Wesleyan University Press, Middletown (1961)

    Google Scholar 

  38. Kyburg, H.E., Jr., Teng, C.M., Wheeler, G.R.: Conditionals and consequences. J. Appl. Log. 5, 638–650 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  39. Lehmann, D.J., Magidor, M.: What does a conditional knowledge base entail? Artif. Intell. 55(1), 1–60 (1992)

    MathSciNet  MATH  Google Scholar 

  40. Lober, K., Shanks, D.: Is causal induction based on causal power? Critique of Cheng (1997). Psychol. Rev. 107, 195–212 (2000)

    Google Scholar 

  41. Lowe, E.J.: For want of a nail. Analysis 40, 50–52 (1980)

    Article  Google Scholar 

  42. Mackie, J.L.: The transitivity of counterfactuals and causation. Analysis 40, 53–54 (1980)

    Article  Google Scholar 

  43. Over, D.E. Hadjichristidis, C., Evans, J.St.B.T, Handley, S.J., Sloman, S.A.: The probability of causal conditionals. Cognitive Psychol. 54, 62–97 (2007)

    Article  Google Scholar 

  44. Pearl, J.: Probabilistic Reasoning in Intelligent Systems. Morgan Kaufmann, San Mateo (1988)

    Google Scholar 

  45. Pearl, J.: Causality: Models, Reasoning, and Inference. Cambridge University Press, Cambridge (2000)

    MATH  Google Scholar 

  46. Pfeifer, N., Kleiter, G.D.: Coherence and nonmonotonicity in human nonmonotonic reasoning. Synthese 146, 93–109 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  47. Politzer, G., Bonnefon, J.F.: Two varieties of conditionals and two kinds of defeaters help reveal two fundamental types of reasoning. Mind Lang. 21, 484–503 (2006)

    Google Scholar 

  48. Poole, D.: The effect of knowledge on belief: conditioning, specificity and the lottery paradox in default reasoning. Artif. Intell. 49, 281–307 (1991)

    Article  MathSciNet  MATH  Google Scholar 

  49. Salmon, W.C.: Causality and Explanation. Oxford University Press, New York (1998)

    Book  Google Scholar 

  50. Walley, P.: Statistical Reasoning with Imprecise Probabilities. Chapman and Hall, New York (1991)

    MATH  Google Scholar 

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Authors and Affiliations

  1. CLLE (CNRS, UTM, EPHE), Maison de la Recherche, 5 al. A. Machado, 31058, Toulouse Cedex 9, France

    Jean-François Bonnefon & Rui Da Silva Neves

  2. IRIT (CNRS, UPS), Université Paul Sabatier, 118 Route de Narbonne, 31062, Toulouse Cedex 9, France

    Didier Dubois & Henri Prade

Authors
  1. Jean-François Bonnefon
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  2. Rui Da Silva Neves
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  3. Didier Dubois
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  4. Henri Prade
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Corresponding author

Correspondence to Henri Prade.

Additional information

This research was supported by a grant from the Agence Nationale de la Recherche, project number NT05-3-44479.

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Bonnefon, JF., Da Silva Neves, R., Dubois, D. et al. Qualitative and quantitative conditions for the transitivity of perceived causation:. Ann Math Artif Intell 64, 311–333 (2012). https://doi.org/10.1007/s10472-012-9291-0

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