Learning from Informants: Relations between Learning Success Criteria

Learning from positive and negative information, so-called
informants, being one of the models for human and machine learning
introduced by Gold [1967], is investigated. Particularly, naturally arising
questions about this learning setting, originating in results on learning
from solely positive information, are answered.
By a carefully arranged argument learners can be assumed to only change their hypothesis in case it is inconsistent with the data (such a learning behavior is called conservative). The deduced main theorem states the relations between the most important delayable learning success criteria, being the ones not ruined by a delayed in time hypothesis output.
Additionally, our investigations concerning the non-delayable requirement of consistent learning underpin the claim for delayability being the right structural property to gain a deeper understanding concerning the nature of learning success criteria.
Moreover, we obtain an anomalous hierarchy when allowing for an increasing finite number of anomalies of the hypothesized language by the learner compared with the language to be learned.
In contrast to the vacillatory hierarchy for learning from solely positive
information, we observe a duality depending on whether infinitely many vacillations between different (almost) correct hypotheses are still considered a successful learning behavior.