Rich Classes Inferrable from Positive Data: Length-Bounded Elementary Formal Systems

AbstractInductive inference from positive data is shown to be remarkably powerful using the framework of elementary formal systems. An elementary formal system, EFS for short, is a kind of logic program on Σ+ consisting of finitely many axioms. Any context-sensitive language is definable by a restricted EFS, called a length-bounded EFS. Length-bounded EFSs with at most n axioms are considered, and it is shown that inductive inference from positive data works successfully for their models as well as for their languages. From this it follows that any class of logic programs, such as Prolog programs, corresponding to length-bounded EFSs can be inferred from positive facts