Similarity Orders from Causal Equations

  • Johannes Marti
  • Riccardo Pinosio
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8761)


The purpose of this paper is to demonstrate that, contrary to the received wisdom, causal reasoning can be formalized wholly within the framework of Lewis’ conditional logic. To this aim we simulate causal reasoning based on structural equations in Lewis’ order semantics. This reduction is based on a formalization of an intuitive idea for computing relative similarity between worlds. Worlds are the more similar the more they satisfy the same relevant propositions, where relevance is a comparative notion represented by a preorder. In the context of causal reasoning this relevance order on propositions depends on the causal structure of the problem domain.


Causal reasoning conditional logic counterfactual conditionals non-monotonic reasoning similarity orders structural equations 


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  1. 1.
    Coste-Marquis, S., Lang, J., Liberatore, P., Marquis, P.: Expressive power and succinctness of propositional languages for preference representation. In: Dubois, D., Welty, C.A., Williams, M.-A. (eds.) KR, pp. 203–212. AAAI Press (2004)Google Scholar
  2. 2.
    Halpern, J.Y.: From causal models to counterfactual structures. Review of Symbolic Logic 6(2), 305–322 (2013)MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Kratzer, A.: Partition and revision: The semantics of counterfactuals. Journal of Philosophical Logic 10(2), 201–216 (1981)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Lewis, D.: Counterfactuals. Blackwell Publishers (1973)Google Scholar
  5. 5.
    Lewis, D.: Counterfactual dependence and time’s arrow. Noûs 13(4), 455–476 (1979)CrossRefGoogle Scholar
  6. 6.
    Lewis, D.: Ordering semantics and premise semantics for counterfactuals. Journal of Philosophical Logic 10(2), 217–234 (1981)MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Marti, J., Pinosio, R.: Topological semantics for conditionals. In: Punčochář, V., Švarný, P. (eds.) The Logica Yearbook 2013. College Publications (to appear)Google Scholar
  8. 8.
    Pearl, J.: Causality: Models, Reasoning, and Inference. Cambridge University Press (2000)Google Scholar
  9. 9.
    Schulz, K.: Minimal Models in Semantics and Pragmatics: Free Choice, Exhaustivity, and Conditionals. PhD thesis, University of Amsterdam (2007)Google Scholar
  10. 10.
    Schulz, K.: “If you’d wiggled A, then B would’ve changed” - Causality and counterfactual conditionals. Synthese 179(2), 239–251 (2011)CrossRefzbMATHGoogle Scholar
  11. 11.
    Simon, H.A., Rescher, N.: Cause and counterfactual. Philosophy of Science 33(4), 323–340 (1966)CrossRefGoogle Scholar
  12. 12.
    Tichý, P.: A counterexample to the Stalnaker-Lewis analysis of counterfactuals. Philosophical Studies 29(4), 271–273 (1976)CrossRefGoogle Scholar
  13. 13.
    Veltman, F.: Prejudices, presuppositions, and the theory of counterfactuals. In: Groenendijk, J., Stokhof, M. (eds.) Amsterdam Papers in Formal Grammar, vol. 1, pp. 248–282. Centrale Interfaculteit, Universiteit van Amsterdam (1976)Google Scholar
  14. 14.
    Veltman, F.: Logics for Conditionals. PhD thesis, University of Amsterdam (1985)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Johannes Marti
    • 1
  • Riccardo Pinosio
    • 1
  1. 1.ILLCUniversity of AmsterdamThe Netherlands

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