Inductive Inference Machines That Can Refute Hypothesis Spaces

Abstract

This paper intends to give a theoretical foundation of machine discovery from examples. We point out that the essence of a logic of machine discovery is the refutability of the entire spaces of hypotheses. We discuss this issue in the framework of inductive inference of length-bounded elementary formal systems (EFS's, for short), which are a kind of logic programs over strings of characters and correspond to context-sensitive grammars in Chomsky hierarchy. We first present some characterization theorems on inductive inference machines that can refute hypothesis spaces. Then we show differences between our inductive inference and other related inferences such as in the criteria of reliable identification, finite identification and identification in the limit. Finally we show that for any n , the class, i.e. hypothesis space, of length-bounded EFS's with at most n axioms is inferable in our sense, that is, the class is refutable by a consistently working inductive inference machine. This means that sufficiently large hypothesis spaces are identifiable and refutable.