Abstract
This paper settles a question about “prudent” “vacillatory” identification of languages. Consider a scenario in which an algorithmic deviceM is presented with all and only the elements of a languageL, andM conjectures a sequence, possibly infinite, of grammars. Three different criteria for success ofM onL have been extensively investigated in formal language learning theory. IfM converges to a single correct grammar forL, then the criterion of success is Gold's seminal notion ofTxtEx-identification. IfM converges to a finite number of correct grammars forL, then the criterion of success is calledTxtFex-identification. Further, ifM, after a finite number of incorrect guesses, outputs only correct grammars forL (possibly infinitely many distinct grammars), then the criterion of success is known asTxtBc-identification. A learning machine is said to beprudent according to a particular criterion of success just in case the only grammars it ever conjectures are for languages that it can learn according to that criterion. This notion was introduced by Osherson, Stob, and Weinstein with a view to investigating certain proposals for characterizing natural languages in linguistic theory. Fulk showed that prudence does not restrictTxtEx-identification, and later Kurtz and Royer showed that prudence does not restrictTxtBc-identification. This paper shows that prudence does not restrictTxtFex-identification.
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References
M. Blum. A machine independent theory of the complexity of recursive functions.Journal of the Association for Computing Machinery, 14:322–336, 1967.
L. Blum and M. Blum. Toward a mathematical theory of inductive inference.Information and Control, 28:125–155, 1975.
R. Brown and C. Hanlon. Derivational complexity and the order of acquisition in child speech. In J. R. Hayes, editor,Cognition and the Development of Language. Wiley, New York, 1970.
J. Case. The power of vacillation. In D. Haussler and L. Pitt, editors,Proceedings of the Workshop on Computational Learning Theory, pages 133–142. Morgan Kaufmann, Los Altos, CA, 1988. Expanded in [5].
J. Case. The Power of Vacillation in Language Learning. Technical Report 93-08, University of Delaware, 1992. Expands on [4]; journal article under review.
J. Case and C. Lynes. Machine inductive inference and language identification. In M. Nielsen and E. M. Schmidt, editors,Proceedings of the 9th International Colloquium on Automata, Languages and Programming, volume 140, pages 107–115. Springer-Verlag, Berlin, 1982.
M. Demetras, K. Post, and C. Snow. Feedback to first language learners: the role of repetitions and clarification questions.Journal of Child Language, 13:275–292, 1986.
M. Fulk. A Study of Inductive Inference Machines. Ph.D. thesis, SUNY at Buffalo, 1985.
M. Fulk. Prudence and other conditions on formal language learning.Information and Computation, 85:1–11, 1990.
E. M. Gold. Language identification in the limit.Information and Control, 10:447–474, 1967.
K. Hirsh-Pasek, R. Treiman, and M. Schneiderman. Brown and Hanlon revisited: mothers' sensitivity to ungrammatical forms.Journal of Child Language, 11:81–88, 1984.
J. Hopcroft and J. Ullman.Introduction to Automata Theory Languages and Computation. Addison-Wesley, Reading, MA, 1979.
K. Jantke and H. Beick. Combining postulates of naturalness in inductive inference.Electronische Informationverarbeitung und Kybernetik, 17:465–484, 1981.
S. A. Kurtz and J. S. Royer. Prudence in language learning. In D. Haussler and L. Pitt, editors,Proceedings of the Workshop on Computational Learning Theory, pages 143–156. Morgan Kaufmann, Los Altos, CA, 1988.
M. Machtey and P. Young.An Introduction to the General Theory of Algorithms. North-Holland, New York, 1978.
D. Osherson, M. Stob, and S. Weinstein. Learning strategies.Information and Control, 53:32–51, 1982.
D. Osherson, M. Stob, and S. Weinstein. Learning theory and natural language.Cognition, 17:1–28, 1984.
D. Osherson and S. Weinstein. Criteria of language learning.Information and Control, 52:123–138, 1982.
D. Osherson and S. Weinstein. A note on formal learning theory.Cognition, 11:77–88, 1982.
D. Osherson and S. Weinstein. On the study of first language acquisition.Journal of Mathematical Psychology, in press, 1995.
S. Penner. Parental responses to grammatical and ungrammatical child utterances.Child Development, 58:376–384, 1987.
S. Pinker. Formal models of language learning.Cognition, 7:217–283, 1979.
H. Rogers. Gödel numberings of partial recursive functions.Journal of Symbolic Logic, 23:331–341, 1958.
H. Rogers.Theory of Recursive Functions and Effective Computability. McGraw-Hill, New York, 1967. Reprinted, MIT Press, Cambridge, MA, 1987.
K. Wexler. On extensional learnability.Cognition, 11:89–95, 1982.
K. Wexler and P. Culicover.Formal Principles of Language Acquisition. MIT Press, Cambridge, MA, 1980.
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Jain, S., Sharma, A. Prudence in vacillatory language identification. Math. Systems Theory 28, 267–279 (1995). https://doi.org/10.1007/BF01303059
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DOI: https://doi.org/10.1007/BF01303059