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The paper deals with the following problem: is returning to wrong conjectures necessary to achieve full power of algorithmic learning? Returning to wrong conjectures complements the paradigm of U-shaped learning [3,7,9,24,29] when a learner returns to old correct conjectures. We explore our problem for classical models of learning in the limit from positive… (More)

U-shaped learning is a learning behaviour in which the learner first learns a given target behaviour, then unlearns it and finally relearns it. Such a behaviour, observed by psychologists, for example, in the learning of past-tenses of English verbs, has been widely discussed among psychologists and cognitive scientists as a fundamental example of the… (More)

U-shaped learning behaviour in cognitive development involves learning, unlearning and relearning. It occurs, for example, in learning irregular verbs. The prior cog-nitive science literature is occupied with how humans do it, for example, general rules versus tables of exceptions. This paper is mostly concerned with whether U-shaped learning behaviour may… (More)

We define a direct translation from finite rooted trees to finite natural functions which shows that the Worm Principle introduced by Lev Beklemishev is equivalent to a very slight variant of the well-known Kirby-Paris' Hydra Game. We further show that the elements in a reduction sequence of the Worm Principle determine a bad sequence in the… (More)

We investigate a new paradigm in the context of learning in the limit, namely, learning correction grammars for classes of computably enumerable (c.e.) languages. Knowing a language may feature a representation of it in terms of two grammars. The second grammar is used to make corrections to the first grammar. Such a pair of grammars can be seen as a single… (More)

A U-shaped curve in a cognitive-developmental trajectory refers to a three-step process: good performance followed by bad performance followed by good performance once again. U-shaped curves have been observed in a wide variety of cognitive-developmental and learning contexts. U-shaped learning seems to contradict the idea that learning is a monotonic,… (More)

We initiate the study of the proof complexity of propositional encoding of (weak cases of) concrete independence results. In particular we study the proof complexity of Paris-Harrington's Large Ramsey Theorem. We prove a conditional lower bound in Resolution and a quasipolynomial upper bound in bounded-depth Frege.