Classifying Predicates and Languages

The present paper studies a particular collection of classification problems, i.e., the classification of recursive predicates and languages, for arriving at a deeper understanding of what classification really is. In particular, the classification of predicates and languages is compared with the classification of arbitrary recursive functions and with their learnability. The investigation undertaken is refined by introducing classification within a resource bound resulting in a new hierarchy. Furthermore, a formalization of multi-classification is presented and completely characterized in terms of standard classification. Additionally, consistent classification is introduced and compared with both resource bounded classification and standard classification. Finally, the classification of families of languages that have attracted attention in learning theory is studied, too.