Mapping Monotonic Restrictions in Inductive Inference

TL;DR

This paper explores the learning capabilities of monotonic learners in language learning, revealing key differences and similarities with strongly monotone learners, especially regarding their reliance on information order and the impact of various restrictions.

Contribution

It provides a detailed comparison between monotone and strongly monotone learners under different restrictions, highlighting their behavioral and explanatory differences.

Findings

Explanatory monotone learners nearly preserve pairwise relations seen in strongly monotone learners.

Behaviorally correct monotone learners heavily depend on the order of information, unlike their strongly monotone counterparts.

Monotone learners show significant reliance on information order, contrasting with expectations for behaviorally correct learners.

Abstract

In language learning in the limit we investigate computable devices (learners) learning formal languages. Through the years, many natural restrictions have been imposed on the studied learners. As such, monotonic restrictions always enjoyed particular attention as, although being a natural requirement, monotonic learners show significantly diverse behaviour when studied in different settings. A recent study thoroughly analysed the learning capabilities of strongly monotone learners imposed with memory restrictions and various additional requirements. The unveiled differences between explanatory and behaviourally correct such learners motivate our studies of monotone learners dealing with the same restrictions. We reveal differences and similarities between monotone learners and their strongly monotone counterpart when studied with various additional restrictions. In particular, we show that explanatory monotone learners, although known to be strictly stronger, do (almost) preserve the pairwise relation as seen in strongly monotone learning. Contrasting this similarity, we find substantial differences when studying behaviourally correct monotone learners. Most notably, we show that monotone learners, as opposed to their strongly monotone counterpart, do heavily rely on the order the information is given in, an unusual result for behaviourally correct learners.