6 found
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  1.  69
    On the Necessity of U-Shaped Learning.Lorenzo Carlucci & John Case - 2013 - Topics in Cognitive Science 5 (1):56-88.
    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, cumulative process and thus constitutes a challenge for competing theories of cognitive development and learning. U-shaped behavior in language learning (in particular in learning English past tense) has become a central (...)
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  2.  14
    Worms, Gaps, and Hydras.Lorenzo Carlucci - 2005 - Mathematical Logic Quarterly 51 (4):342-350.
    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 well-quasi-ordering of finite sequences of natural numbers with respect to Friedman's gapembeddability. A characterization of gap-embeddability in terms of provability logic due to Lev Beklemishev (...)
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  3.  15
    A Weak Variant of Hindman’s Theorem Stronger Than Hilbert’s Theorem.Lorenzo Carlucci - 2018 - Archive for Mathematical Logic 57 (3-4):381-389.
    Hirst investigated a natural restriction of Hindman’s Finite Sums Theorem—called Hilbert’s Theorem—and proved it equivalent over \ to the Infinite Pigeonhole Principle for all colors. This gave the first example of a natural restriction of Hindman’s Theorem provably much weaker than Hindman’s Theorem itself. We here introduce another natural restriction of Hindman’s Theorem—which we name the Adjacent Hindman’s Theorem with apartness—and prove it to be provable from Ramsey’s Theorem for pairs and strictly stronger than Hirst’s Hilbert’s Theorem. The lower bound (...)
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  4.  6
    Learning Correction Grammars.Lorenzo Carlucci, John Case & Sanjay Jain - 2009 - Journal of Symbolic Logic 74 (2):489-516.
    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 description of (or grammar for) the language. We call such grammars correction grammars. Correction grammars capture the observable fact that (...)
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  5.  4
    The Strength of Ramsey’s Theorem for Coloring Relatively Large Sets.Lorenzo Carlucci & Konrad Zdanowski - 2014 - Journal of Symbolic Logic 79 (1):89-102.
  6.  5
    A Note on Ramsey Theorems and Turing Jumps.Lorenzo Carlucci & Konrad Zdanowski - 2012 - In S. Barry Cooper (ed.), How the World Computes. pp. 89--95.