Precise induction from statistical data

In inductive reasoning one uses a small set of examined instances to infer global relations. The standard approach is to search for relations that can be verified in all the examined instances, and hypothesize that they hold globally Relations that hold only for a subset of the examined instances were previously used only for statistical inference. In this paper it is shown that this statistical information can also be used to infer relations that hold for all instances. The main result is an algorithm that uses statistics to infer Boolean predicates. The analysis includes an investigation of what statistics are relevant for such inference, and what predicates can be inferred.