Abstract
The present paper settles an open question about ‘prudent’ vacillatory identification of grammars from positive data only.
Consider a scenario in which a learner M is learning a language L from positive data. Three different criteria for success of M on L have been investigated in formal language learning theory. If M converges to a single correct grammar for L, then the criterion of success is Gold's seminal notion of TxtEx-identification. If M converges to a finite number of correct grammars for L, then the criterion of success is called TxtFex-identification. And, if M, after a finite number of incorrect guesses, outputs only correct grammars for L (possibly infinitely many distinct grammars), then the criterion of success is known as TxtBc-identification.
A learner is said to be prudent 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 investigate certain proposals for characterizing natural languages in linguistic theory. Fulk showed that prudence does not restrict TxtEx-identification, and later Kurtz and Royer were able to show that prudence does not restrict TxtBc-identification. The present paper settles this question by showing that prudence does not restrict TxtFex-identification.
Preview
Unable to display preview. Download preview PDF.
References
L. Blum and M. Blum. Toward a mathematical theory of inductive inference. Information and Control, 28:125–155, 1975.
M. Blum. A machine independent theory of the complexity of recursive functions. Journal of the ACM, 14:322–336, 1967.
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 Publishers, Inc., 1988.
J. Case and C. Lynes. Machine inductive inference and language identification. Lecture Notes in Computer Science, 140:107–115, 1982.
M. Fulk. A Study of Inductive Inference machines. PhD 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.
J. Hopcroft and J. Ullman. Introduction to Automata Theory Languages and Computation. Addison-Wesley Publishing Company, 1979.
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 Publishers, Inc., 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. Ideal learning machines. Cognitive Science, 6:277–290, 1982.
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, M. Stob, and S. Weinstein. Systems that Learn, An Introduction to Learning Theory for Cognitive and Computer Scientists. MIT Press, Cambridge, Mass., 1986.
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.
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 1987.
K. Wexler and P. Culicover. Formal Principles of Language Acquisition. MIT Press, Cambridge, Mass, 1980.
K. Wexler. On extensional learnability. Cognition, 11:89–95, 1982.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1993 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Jain, S., Sharma, A. (1993). Prudence in vacillatory language identification (Extended abstract). In: Doshita, S., Furukawa, K., Jantke, K.P., Nishida, T. (eds) Algorithmic Learning Theory. ALT 1992. Lecture Notes in Computer Science, vol 743. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-57369-0_36
Download citation
DOI: https://doi.org/10.1007/3-540-57369-0_36
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-57369-2
Online ISBN: 978-3-540-48093-8
eBook Packages: Springer Book Archive