Saving the phenomena: Requirements that inductive inference machines not contradict known data
Mark A. Fulk · Information and Computation · 1988
Three kinds of restrictions on inductive inference machines (IIMs) are considered: postdictive completeness, postdictive consistency, and reliability. It is shown that postdictively consistent IIMs can be effectively replaced with post-dictively complete IIMs that succeed to at least the same degree. Various loosenings of the notions of postdictive completeness and reliability are considered, and a pair of related triangular hierarchies is exhibited; IIMs higher (or to the right) in the hierarchies are less restricted and capable of learning more than IIMs lower or to the left. Various conjectures and older results are obtained as corollaries.