I read your mesg of last Monday and, unfortunately,
I could not understand most of what you were trying to
express. I must report, however, that if I understood correctly
what you said about "Pearl-style diagrams", then
your statement is regretfully false.
Here is what you wrote:
3. The questions in par. 2 above bring me to an alternative to the sort
of picture of inference that I have sketched above: Pearl-style causal
reasoning. Isn't it the case that Pearl-style causal reasoning --
despite being avowedly _"causal"_ -- isn't it the case that Pearl-style
causal reasoning fails to "capture" the complexity of the sort of
(jumbled) causal reasoning that is involved in my last example? Pearl's
diagrams look "causal" to me _only_ in the sense that they posit that
all events have an antecedent cause or causes. In every other respect,
his diagrams make the links between events or propositions look like
relative frequencies rather than like the sort of complex relationships
that one finds in even simple "real" causal hypotheses such as F = MA.
My response:
I am not sure what need be "captured" in what you call
"the complexity of the sort of (jumbled) causal reasoning
that is involved in my last example? "
but I am very very sure that the diagrams I am using
are causal in every respect, that the
the links between events or propositions have little to do
with relative frequencies, and that
your "real" causal hypotheses such as F = MA
can be incorporated properly and formally into those
diagrams.
I would encourage you to read some of the latest literature
on causal diagrams, eg., Proceedings of UAI 1990-1998,
Biometrika, Dec. 1995, AIJ 1997, etc. or have a glimpse at my
web site http://bayes.cs.ucla.edu/jp_home.html
You will be pleased to discover there methods of
formalizing, processing and learning many features
of causal relationships , including effects of intervetions,
counterfactuals, confounding, causal explanations, etc.
including even measures of legal responsibility and
"actual causation" which are of interest to
legal scholars.
I hope you take the time to read this literature,
Enjoy,
=========Judea