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rhollerith_dot_com comments on Open Thread: July 2010 - Less Wrong
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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.