Mapping Monotonic Restrictions in Inductive Inference

In inductive inference we investigate computable devices (learners) learning formal languages. In this work, we focus on monotonic learners which, despite their natural motivation, exhibit peculiar behaviour. A recent study analysed the learning capabilities of strongly monotone learners in various settings. The therein unveiled differences between explanatory (syntactically converging) and behaviourally correct (semantically converging) such learners motivate our studies of monotone learners in the same settings. While the structure of the pairwise relations for monotone explanatory learning is similar to the strongly monotone case (and for similar reasons), for behaviourally correct learning a very different picture emerges. In the latter setup, we provide a self-learning class of languages showing that monotone learners, as opposed to their strongly monotone counterpart, do heavily rely on the order in which the information is given, an unusual result for behaviourally correct learners.