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Abstract

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.