Team Learning and Quasi-closedness in Inductive Inference ?

This paper investigates relations between team learning and a quasi-closedness property inherent in many identiication types considered in inductive inference. This property is as follows: there exists such n that, if every union of n ?1 classes out of U1; : : : ; Un is identiiable, so is the union of all n classes. This property can be formulated in terms of team learning, but in practice the research in team learning have followed one path, while investigations of the quasi-closedness property have led along another path. Here we investigate the connection between quasi-closedness and team learning more closely. We show that the numbers n for which the quasi-closedness holds determine the largest element of the so-called hierarchy of success ratios of an identiication type. We also investigate quasi-closedness of team identiication types themselves. Some results are related with probabilistic learning.