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  1. Lorenzo Carlucci & John Case (2013). On the Necessity of U-Shaped Learning. 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. John Case & Sanjay Jain (2011). Rice and Rice-Shapiro Theorems for Transfinite Correction Grammars. Mathematical Logic Quarterly 57 (5):504-516.
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  3. Lorenzo Carlucci, John Case & Sanjay Jain (2009). Learning Correction Grammars. 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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  4. John Case, Keh-Jiann Chen, Sanjay Jain, Wolfgang Merkle & James S. Royer (2006). Generality's Price: Inescapable Deficiencies in Machine-Learned Programs. Annals of Pure and Applied Logic 139 (1):303-326.
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  5. Andris Ambainis, John Case, Sanjay Jain & Mandayam Suraj (2004). Parsimony Hierarchies for Inductive Inference. Journal of Symbolic Logic 69 (1):287-327.
    Freivalds defined an acceptable programming system independent criterion for learning programs for functions in which the final programs were required to be both correct and "nearly" minimal size, i.e., within a computable function of being purely minimal size. Kinber showed that this parsimony requirement on final programs limits learning power. However, in scientific inference, parsimony is considered highly desirable. A lim-computablefunction is (by definition) one calculable by a total procedure allowed to change its mind finitely many times about its output. (...)
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  6. John Case (1997). Jill Kraye. In Jill Kraye (ed.), Cambridge Translations of Renaissance Philosophical Texts. Cambridge University Press. 1--59.
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  7. Ganesh Baliga, John Case, Sanjay Jain & Mandayam Suraj (1994). Machine Learning of Higher-Order Programs. Journal of Symbolic Logic 59 (2):486-500.
    A generator program for a computable function (by definition) generates an infinite sequence of programs all but finitely many of which compute that function. Machine learning of generator programs for computable functions is studied. To motivate these studies partially, it is shown that, in some cases, interesting global properties for computable functions can be proved from suitable generator programs which cannot be proved from any ordinary programs for them. The power (for variants of various learning criteria from the literature) of (...)
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  8. John Case (1991). Effectivizing Inseparability. Mathematical Logic Quarterly 37 (7):97-111.
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  9. John Case (1986). Learning Machines. In William Demopoulos (ed.), Language Learning and Concept Acquisition. Ablex.
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  10. John Case (1976). Sortability and Extensibility of the Graphs of Recursively Enumerable Partial and Total Orders. Mathematical Logic Quarterly 22 (1):1-18.
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  11. John Case (1974). Maximal Arithmetical Reducibilities. Mathematical Logic Quarterly 20 (13‐18):261-270.
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  12. John Case (1971). Enumeration Reducibility and Partial Degrees. Annals of Mathematical Logic 2 (4):419-439.
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