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rhollerith_dot_com comments on Open Thread: July 2010 - Less Wrong
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You're probably right, Silas, that "YW" means "Y and W" (or "y and w" or what have you), but you confuse the matter by stating falsely that the original poster (beriukay) was right in his guess: if it was a union operation, Pearl would write it "Y cup W" or "y or w" or some such.
I do not have the book in front of me, beriukay, so that is the only guidance I can give you given what you have written so far.
Added. I now recall the page you refer to: there are about a dozen "laws" having to do with conditional independence. Now that I remember, I am almost certain that "YW" means "Y intersection W".
Sorry, I'm bad about that terminology. Thanks for the correction.
First, thanks for taking an interest in my question. I just realized that instead of typing my question into a different substrate, google likely had a scan of the page in question. I was correct. And unless I am mistaken, when he introduces his probability axioms he explicitly stated that he would use a comma to indicate intersection.
I am afraid I cannot agree with you.
Have you succeeded in your stated intention of "deriving the property of Decomposition using the given definition (X || Y | Z) iff P( x | y,z ) = P( x | z ), and the basic axioms of probability theory"?
If you wish to continue discussing this problem with me, I humbly suggest that the best way forward is for you to show me your proof of that. And we might take the discussion to email if you like.
It is great that you are studying Pearl.