On Learning Formulas in the Limit and With Assurance

We consider the learning of formulas in the model of [2, 5]. We show that, in this model, a formula f can be learned in the limit if and only if :f can be learned with assurance. 1 Introduction Barzdins, Freivalds and Smith[2] introduced a learning model for inferring formulas of first order predicate logic from elementary facts. In their model, the learner receives an enumeration of elementary facts that are true in some model. The task of the learner is to synthesize formulas that are true in this model from these facts. They considered three variants of this model: finite learning, learning in the limit and learning with assurance levels (derived from corresponding models in Gold-style inductive inference[3, 4]: finite learning[6], learning in the limit[3] and learning with confidence[1]). The three versions of the model differ by whether (and how) the learner is allowed to change its guesses. In finite learning, once a formula is output, no changes can be made. In learning in..