I'm starting using P-DL as an abbreviation for Probabilistic DL. Hope that's clear enough.
In my last post I whined about the complications of adding complex probabilistic formulas to P-DL without any good justification that they are actually needed. Let me now propose something else that seems to be easier to implement and might even be more useful.
Recall that Pronto needs numbers (intervals) for each of its conditional constraints. In some cases, however, it might make sense to express *relative* probabilistic constraints w/o any reference to numbers. For example: Given the symptoms, the chance of having disease A is twice as high as the chance of having B. So, we may not be willing to commit to numbers (or may not even know the numbers!) but still want to express the constraint. Why not to allow this?
This can be represented by expressions of the form:
k1*P(psi1|phi1)[l1,u1]+...+kn*P(psin|phin)[ln,un] >= 0
The semantics is also pretty clear - we just need to impose an extra restriction on the possible probability distributions. But this is just *one* inequality so allowing such expressions is no harder than supporting constraints themselves. That's good.
Next step - to implement it? Yes, I need to sort out nominals first.. =yawn=
Friday, November 23, 2007
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1 comments:
Good post.
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