## Automatic Derivation of Probabilistic Inference Rules

Manfred Jaeger
A probabilistic inference rule is a general rule that
provides bounds on a target probability given constraints on
a number of input probabilities. Example: from
$P(A | B) \leq r$\ infer $P(\neg A | B) \in [1-r,1]$. Rules of
this kind have been studied extensively as a deduction
method for propositional probabilistic logics. Many different
rules have been proposed, and their validity proved --
often with substantial effort. Building on previous work
by T. Hailperin, in this paper we show that probabilistic
inference rules can be derived automatically, i.e. given
the input constraints and the target probability, one
can automatically derive the optimal bounds on the target
probability as a functional expression in the parameters
of the input constraints.

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