Charles and Peter, Just for the record, the Halpern-Pearl definition of actual causality is a 0-1 definition. Either A is a cause of B or its not. We can then certainly talk about the probability that A is an actual cause of B, or refine the definition to responsibility (as in the Chockler-Halpern paper), both of which give you a way of talking about degrees that are between 0 and 1.
And Charles, one point you make below is not quite right: > Hi Peter, > > > nGood questions. > > On Sun, 19 Oct 2003, Peter Tillers wrote: > }1. Are the following two separate responses by Charles Twardy and Joseph > }Halpern to Lotfi Zadeh consistent?: > } [Halpern says causal modeling supports degree of responsibility but not > } degree of causation, while Twardy says it supports degree of > } causation as well.] > > I think we just chose different aspects, and that your reconciliation > worked pretty well. But I think another main difference is whether you use > the framework to answer questions of actual or "token" causation which is > more about assigning responsibility (What caused the fire?), or whether > you use it to answer questions about general or "type" causation (Does > smoking cause lung cancer, in general?) > > Halpern's work with Pearl (that I know) has concentrated on actual or > token causation. Either C contributed to E or not, but not all causes of E > contributed equally. I share the intuition that perhaps not all causes contribute equally, but the Halpern-Pearl definition of causality does not discuss the degree to which something contributes. It is possible that different causes will have different degrees of responsibility though, according to the Chockler-Halpern definition. > (They also analyze what it means for a set of causes to be "the" > actual cause.) That's not quite true. The definition talks about whether a conjunction X1=x1 & X2 = x2 ... & Xn=xn is a cause of some event \phi, but then we conjectured (and Eiter/Lukasiwecz and Hopkins independently proved) that the conjunction had to be size one. That is, you can never get a nontrivial conjunction being a cause. I don't believe we ever talk about a set of causes being "the" cause. (If ever say "the" cause in the paper, it should be corrected! It's always "a" cause.) > Work on general causation (most of Pearl 2000) is more clearly a matter of > degree: C causes E if there is some state of the model where C can affect > the probability distribution on E. (Or, if you want to talk about > particular states rather than variables, you may distinguish promoting > from preventing.) > > One other issue: you can use the framework and still believe in > determinism (as I think Pearl does). Then the probabilities are either > uncertainties about the exogenous variables or the models. That's exactly right. That's how we can talk about probability of actual causation. > Pearl and > Halpern assume determinism for actual causation. But the general framework > does not need to make that assumption. You may be right, but it's not obvious exactly how the definitions should be modified if the structural equations are probabilistic rather than deterministic. (I can imagine a number of ways that this could be done; I don't have any intution as to which would be more appropriate, although I'll admit I haven't thought about it hard.) > -Charles -- Joe
