Children learn their native language by exposure to their linguistic and communicative environment, but apparently without requiring that their mistakes be corrected. Such learning from “positive evidence” has been viewed as raising “logical” problems for language acquisition. In particular, without correction, how is the child to recover from conjecturing an over-general grammar, which will be consistent with any sentence that the child hears? There have been many proposals concerning how this “logical problem” can be dissolved. In this study, we review (...) recent formal results showing that the learner has sufficient data to learn successfully from positive evidence, if it favors the simplest encoding of the linguistic input. Results include the learnability of linguistic prediction, grammaticality judgments, language production, and form-meaning mappings. The simplicity approach can also be “scaled down” to analyze the learnability of specific linguistic constructions, and it is amenable to empirical testing as a framework for describing human language acquisition. (shrink)

We compare the elementary theories of Shannon information and Kolmogorov complexity, the extent to which they have a common purpose, and wherethey are fundamentally different. We discuss and relate the basicnotions of both theories: Shannon entropy, Kolmogorov complexity, Shannon mutual informationand Kolmogorov (``algorithmic'') mutual information. We explainhow universal coding may be viewed as a middle ground betweenthe two theories. We consider Shannon's rate distortion theory, whichquantifies useful (in a certain sense) information.We use the communication of information as our guiding motif, (...) and we explain howit relates to sequential question-answer sessions. (shrink)

We argue that confusability between items should be distinguished from generalization between items. Shepard's data concern confusability, but the theories proposed by Shepard and by Tenenbaum & Griffiths concern generalization, indicating a gap between theory and data. We consider the empirical and theoretical work involved in bridging this gap. [Shepard; Tenenbaum & Griffiths].

Remembering Kolmogorov Content Type Journal Article Pages 1-3 DOI 10.1007/s11016-011-9540-6 Authors Paul M. B. Vitányi, CWI, Science Park 123, 1098 XG Amsterdam, The Netherlands Journal Metascience Online ISSN 1467-9981 Print ISSN 0815-0796.