Classifying Predicates and Languages

The present paper studies a particular collection of classi cation problems, i.e., the classi cation of recursive predicates and languages, for arriving at a deeper understanding of what classi cation really is. In particular, the classi cation of predicates and languages is compared with the classi cation of arbitrary recursive functions and with their learnability. The investigation undertaken is re ned by introducing classi cation within a resource bound resulting in a new hierarchy. Furthermore, a formalization of multi{classi cation is presented and completely characterized in terms of standard classi cation. Additionally, consistent classi cation is introduced and compared with both resource bounded classi cation and standard classi cation. Finally, the classi cation of families of languages that have attracted attention in learning theory is studied, too. A preliminary version of this paper appeared at the rst European Workshop on Computational Learning Theory