Incremental learning with temporary memory

In the inductive inference framework of learning in the limit, a variation of the bounded example memory (Bem) language learning model is considered. Intuitively, the new model constrains the learner’s memory not only in how much data may be retained, but also in how long that data may be retained. More specifically, the model requires that, if a learner commits an example x to memory in some stage of the learning process, then there is some subsequent stage for which x no longer appears in the learner’s memory. This model is called temporary example memory (Tem) learning. In some sense, it captures the idea that memories fade. Many interesting results concerning the Tem-learning model are presented. For example, there exists a class of languages that can be identified by memorizing k + 1 examples in the Tem sense, but that cannot be identified by memorizing k examples in the Bem sense. On the other hand, there exists a class of languages that can be identified by memorizing just 1 example in the Bem sense, but that cannot be identified by memorizing any number of examples in the Tem sense. (The proof of this latter result involves an infinitary self-reference argument.) Results are also presented concerning the special cases of: learning indexable classes of languages, and learning (arbitrary) classes of infinite languages.