Max-Min Chaining of Weighted Causal Assertions is Loop Free

S. W. Ng, Adrian Walker

If a system uses assertions of the general form x causes y, (e.g. MYCIN rules) then loop situations in which X1 causes X2, X2 causes X3, .... , Xn causes X1, are, intuitively, best avoided. If an assertion has an attached confidence weight, as in x(0.8)-causes y , then one can choose to say that the confidence in a chain of such assertions is as strong as the weakest link in the chain. If there are several chains of assertions from X to Z, then one can choose to say that X causes Z with a confidence equal to that of the strongest chain. From these choices, it follows that the confidence that X causes Z corresponds to a loop-free chain of assertions. This is true even if there are chains from X to Z with common subchains and loops within loops. An algorithm for computing the confidence is described.

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