Lorenzo Carlucci

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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)
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 cognitive science literature is occupied with how humans do it, for example, general rules versus tables of exceptions. This paper is mostly concerned with whether Ushaped learning behaviour may be(More)
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)
We construct long sequences of braids that are descending with respect to the standard order of braids (“Dehornoy order”), and we deduce that, contrary to all usual algebraic properties of braids, certain simple combinatorial statements involving the braid order are true, but not provable in the subsystems IΣ1 or IΣ2 of the standard Peano system. It has(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)
The f -regressive Ramsey number R f (d, n) is the minimum N such that every colouring of the d-tuples of an N -element set mapping each x1, . . . , xd to a colour ≤ f(x1) contains a min-homogeneous set of size n, where a set is called min-homogeneous if every two d-tuples from this set that have the same smallest element get the same colour. If f is the(More)