Characterizations of Class Preserving Monotonic and Dual Monotonic Language Learning

The present paper deals with monotonic and dual monotonic language learning from positive as well as from positive and negative examples. The three notions of monotonicity re ect di erent formalizations of the requirement that the learner has to always produce better and better generalizations when fed more and more data on the concept to be learnt. The three versions of dual monotonicity describe the concept that the inference device has to exclusively produce specializations that t better and better to the target language. We characterize strong{monotonic, monotonic, weak{monotonic, dual strong{monotonic, dual monotonic and monotonic & dual monotonic as well as nite language learning from positive data in terms of recursively generable nite sets.