Hasso-Plattner-Institut25 Jahre HPI
Hasso-Plattner-Institut25 Jahre HPI

Vanja Doskoč

"Mapping Restrictions in Behaviourally Correct Learning"

In this thesis, we investigate language learning in the formalisation of Gold (1967). Here, a learner, being successively presented all information of a target language, conjectures which language it believes to be shown. Once these hypotheses converge syntactically to a correct explanation of the target language, the learning is considered successful. Fittingly, this is termed explanatory learning. To model learning strategies, we impose restrictions on the hypotheses made, for example requiring the conjectures to follow a monotonic behaviour. This way, we can study the impact a certain restriction has on learning.

Recently, the literature shifted towards map charting. Here, various seemingly unrelated restrictions are contrasted, unveiling interesting relations between them. The results are then depicted in maps. For explanatory learning, the literature already provides maps of common restrictions for various forms of data presentation.

In the case of behaviourally correct learning, where the learners are required to converge semantically instead of syntactically, the same restrictions as in explanatory learning have been investigated. However, a similarly complete picture regarding their interaction has not been presented yet.

In this thesis, we transfer the map charting approach to behaviourally correct learning. In particular, we complete the partial results from the literature for many well-studied restrictions and provide full maps for behaviourally correct learning with different types of data presentation. We also study properties of learners assessed important in the literature. We are interested whether learners are consistent, that is, whether their conjectures include the data they are built on. While learners cannot be assumed consistent in explanatory learning, the opposite is the case in behaviourally correct learning. Even further, it is known that learners following different restrictions may be assumed consistent. We contribute to the literature by showing that this is the case for all studied restrictions.

We also investigate mathematically interesting properties of learners. In particular, we are interested in whether learning under a given restriction may be done with strongly Bc-locking learners. Such learners are of particular value as they allow to apply simulation arguments when, for example, comparing two learning paradigms to each other. The literature gives a rich ground on when learners may be assumed strongly Bc-locking, which we complete for all studied restrictions.