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  1.  20
    (1 other version)Enumeration reducibility and partial degrees.John Case - 1971 - Annals of Mathematical Logic 2 (4):419-439.
  2. 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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  3.  17
    (1 other version)Maximal Arithmetical Reducibilities.John Case - 1974 - Mathematical Logic Quarterly 20 (13‐18):261-270.
  4. Parsimony hierarchies for inductive inference.Andris Ambainis, John Case, Sanjay Jain & Mandayam Suraj - 2004 - 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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  5.  44
    Machine learning of higher-order programs.Ganesh Baliga, John Case, Sanjay Jain & Mandayam Suraj - 1994 - 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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  6.  35
    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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  7.  3
    Ancilla philosophiae, seu Epitome in octo libros Physicorum Aristotelis, authore Jo. Caso,..John Case & Joseph Barnes - 1599 - Excudebat Iosephus Barnesius.
  8.  1
    Constructivity conditions on immune sets.John Case - forthcoming - Archive for Mathematical Logic:1-23.
    Definitionally: _strongly effectively immune_ sets are infinite and their c.e. subsets have _maximums_ effectively bounded in their c.e. indices; whereas, for _effectively immune_ sets, their c.e. subsets’ _cardinalities_ are what’re effectively bounded. This definitional difference between these two kinds of sets is very nicely paralleled by the following difference between their _complements_. McLaughlin: _strongly_ effectively immune sets can_not_ have _immune complements_; whereas, the main theorem herein: _effectively_ immune sets can_not_ have _hyperimmune complements_. Ullian: _effectively_ immune sets _can_ have _effectively_ immune (...)
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  9.  54
    (1 other version)Effectivizing Inseparability.John Case - 1991 - Mathematical Logic Quarterly 37 (7):97-111.
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  10.  35
    Generality’s price: Inescapable deficiencies in machine-learned programs.John Case, Keh-Jiann Chen, Sanjay Jain, Wolfgang Merkle & James S. Royer - 2006 - Annals of Pure and Applied Logic 139 (1):303-326.
    This paper investigates some delicate tradeoffs between the generality of an algorithmic learning device and the quality of the programs it learns successfully. There are results to the effect that, thanks to small increases in generality of a learning device, the computational complexity of some successfully learned programs is provably unalterably suboptimal. There are also results in which the complexity of successfully learned programs is asymptotically optimal and the learning device is general, but, still thanks to the generality, some of (...)
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  11.  8
    Jill Kraye.John Case - 1997 - In Jill Kraye (ed.), Cambridge translations of Renaissance philosophical texts. New York: Cambridge University Press. pp. 1--59.
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  12. Learning machines.John Case - 1986 - In William Demopoulos (ed.), Language Learning and Concept Acquisition: Foundational Issues. Ablex.
  13.  6
    Lapis philosophicus seu commentarius in 8o lib. phys[icorum] Aristot[elis] in quo arcana physiologiae examinantur.John Case & Joseph Barnes - 1599 - Excudebat Ioseph[Us] Barnesi[Us] Oxoniæ.
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  14.  41
    Rice and Rice-Shapiro Theorems for transfinite correction grammars.John Case & Sanjay Jain - 2011 - Mathematical Logic Quarterly 57 (5):504-516.
    Hay and, then, Johnson extended the classic Rice and Rice-Shapiro Theorems for computably enumerable sets, to analogs for all the higher levels in the finite Ershov Hierarchy. The present paper extends their work to analogs in the transfinite Ershov Hierarchy. Some of the transfinite cases are done for all transfinite notations in Kleene's important system of notations, equation image. Other cases are done for all transfinite notations in a very natural, proper subsystem equation image of equation image, where equation image (...)
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  15.  21
    (1 other version)Sortability and Extensibility of the Graphs of Recursively Enumerable Partial and Total Orders.John Case - 1976 - Mathematical Logic Quarterly 22 (1):1-18.
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  16. Offloading memory to the environment: A quantitative example. [REVIEW]John Case - 2004 - Minds and Machines 14 (3):387-89.
    R.W. Ashby maintained that people and animals do not have to remember as much as one might think since considerable information is stored in the environment. Presented herein is an everyday, quantitative example featuring calculation of the number bits of memory that can be off-loaded to the environment. The example involves one’s storing directions to a friend’s house. It is also argued that the example works with or without acceptance of the extended mind hypothesis. Additionally, a brief supporting argument for (...)
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