Complexity Parameters for First-Order Classes

Marta Arias, Roni Khardon

Abstract: We study several complexity parameters for first-order formulas and their suitability for first order learning models. We show that the standard notion of size is not captured by sets of parameters that are used in the literature. We then identify an alternative notion of size and a simple set of parameters that are useful in this sense. Matching VC-dimension lower bounds complete the picture showing that these parameters are indeed crucial.