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Bayesian Natural Language Semantics and Pragmatics pp 95–116Cite as

On the Probabilistic Notion of Causality: Models and Metalanguages

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Part of the book series: Language, Cognition, and Mind ((LCAM,volume 2))

Abstract

We present some formal, interpreted languages, which are based on propositional logic, but have each a new connective with a semantics based on (conditional) probabilities, which is related to the notion of causality. The first one is well-known as meta-language of Bayesian networks; the other two are new and seem to match better our intuition of a causal connective. We provide definitions of truth and validity, as well as some elementary model theory, in particular focussing on the questions: which properties of probability spaces can be axiomatized by formulas of the new languages, and which not? In particular, we can show that desirable properties of expressive power come at the cost of counterintuitive features.

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Notes

  1. 1.

    We do not define these notions here, and refer the reader to any logic textbook.

  2. 2.

    These definitions roughly coincide with the canonical ones in Kaufmann (2009), though there are some minor differences.

  3. 3.

    Be aware that we allow both arcs and duals; moreover, by acyclicity, at most one of (x, y) and (y, x) is in E; this makes the following statements unique.

  4. 4.

    By the dual of a DAG (E, V) we denote the graph \((E^{-1},V)\), where \((v,v')\in E^{-1}\) iff \((v',v)\in E\). So the dual is the order-theoretic inverse.

  5. 5.

    We write this quotation mark as it does not really reflect the standard meaning of intension.

  6. 6.

    Recall that in this reading, “because A, B” has to be analyzed as: in general, A increases probability of B, and we have the fact (A at a certain time, place etc.) and (B at a certain time, place etc.). Our interpretation of \(C'\) only covers the former portion, not the latter.

References

  • Dehgani, M., Iliev, R., & Kaufmann, S. (2012). Causal explanation and fact mutability in counterfactual reasoning. Mind & Language, 27(1), 55–85.

    Google Scholar 

  • Ebbinghaus, H.-D., & Flum, J. (1995). Finite Model Theory. Perspectives in Mathematical Logic. Springer.

    Google Scholar 

  • Geiger, D., & Pearl, J. (1990). Logical and algorithmic properties of independence and their application to Bayesian networks. Annals of Mathematics and Artificial Intelligence, 2, 165–178.

    Google Scholar 

  • Kaufmann, S. (2009). Conditionals right and left: Probabilities for the whole family. Journal of Philosophical Logic. 38(1), 1–53.

    Google Scholar 

  • Koller, D., & Friedman, N. (2009). Probabilistic graphical models: Principles and techniques. Adaptive computation and machine learning. MIT Press, Cambridge.

    Google Scholar 

  • Pearl, J., (2009). Causality. Models, Reasoning, and Inference. Cambridge University Press, Cambridge.

    Google Scholar 

  • Schurz, G., & Leitgeb, H. (2008). Finitistic and frequentistic approximation of probability measures with or without \(\sigma \)-additivity. Studia Logica, 89(2), 257–283.

    Google Scholar 

  • Verma, T., & Pearl, J. (1990). Equivalence and synthesis of causal models. In P. P. Bonissone, M. Henrion, L. N. Kanal, & J. F. Lemmer, (Eds.), UAI, (pp. 255–270). Elsevier.

    Google Scholar 

  • Wachter, B., Zhang, L., & Hermanns, H. (2007). Probabilistic model checking modulo theories. In QEST, (pp. 129–140). IEEE Computer Society.

    Google Scholar 

  • Woodward, J. (2003). Making things happen: A theory of causal explanation. Oxford: Oxford University Press.

    Google Scholar 

  • Woodward, J. (2006). Sensitive and insensitive causation. The Philosophical Review, 115, 1–50.

    Google Scholar 

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Author information

Authors and Affiliations

  1. Universität Düsseldorf, Dusseldorf, Germany

    Christian Wurm

Authors
  1. Christian Wurm
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Correspondence to Christian Wurm .

Editor information

Editors and Affiliations

  1. ILLC, University of Amsterdam, Amsterdam, The Netherlands

    Henk Zeevat

  2. Fraunhofer Institute for Communication, Information Processing and Ergonomics FKIE, Wachtberg, Germany

    Hans-Christian Schmitz

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Wurm, C. (2015). On the Probabilistic Notion of Causality: Models and Metalanguages. In: Zeevat, H., Schmitz, HC. (eds) Bayesian Natural Language Semantics and Pragmatics. Language, Cognition, and Mind, vol 2. Springer, Cham. https://doi.org/10.1007/978-3-319-17064-0_5

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