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I'm currently reading "Causality: Models, Reasoning, and Inference" by Judea Pearl. Early on, he states that the development assumes that there are no certain entailments, no 1 or 0 probabilities -- that every assignment to variables in a causal model has nonzero probability.

I'm interested in applying some of these ideas to program analysis, where perfect entailment is the norm, and most combinations of assignments are impossible. How much of the theory of causality still applies in this scenario?

One interesting note is that he actually violates his own rule at one point when he talks about modelling a STRIPS-like planning language, and mentions in passing assigning 1 or 0 probabilities in that case.

(Cross-posted from https://cstheory.stackexchange.com/questions/30877/establishing-causality-under-conditions-of-certainty )

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  • $\begingroup$ How much of the theory applies? All of it. The theory depends on the existence of a directed graph structure, not on the stochastic nature of the nodes. $\endgroup$
    – conjugateprior
    Mar 22, 2015 at 13:27
  • $\begingroup$ Now that I'm a bit farther, it appears this is very much false. For example, when trying to apply the do-calculus, I frequently find myself trying to condition on events of probability 0. $\endgroup$
    – James Koppel
    Apr 7, 2015 at 18:29

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From philosophical perspective, I think that you're talking about the concept of causal determinism (Hoefer, 2010), also referred to as deterministic causality. Interesting thoughts (and references) on contrasting probabilistic causality versus deterministic causality can be found in the overview research paper by Yu (2002), specifically in the relevant part of the section "Criticisms" (p. 20-21).

References

Hoefer, C. (2010). Causal determinism. The Stanford Encyclopedia of Philosophy (Spring 2010 Edition), Edward N. Zalta (ed.). Retrieved from http://plato.stanford.edu/entries/determinism-causal

Yu, C. H. (2002). A philosophical investigation of causal interpretation in structural equation models. Retrieved from http://www.creative-wisdom.com/education/hps/causal.pdf

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