Synonyms
Definition
Formal Learning Theory studies systems that convert a stream of data into successive hypotheses about the process generating the data.
Theoretical Background
The basic setup of Formal Learning Theory is illustrated by the following game.
Players: You versus us.
Game pieces: The collection of non-empty finite sets of natural numbers (N = 0, 1, 2, …).
How to play: We will covertly choose one finite set S along with an infinite sequence with range equal to S (e.g., we might choose S = {7, 8, 9} and the sequence 7, 7, 9, 9, 7, 8, 8, 7 …). Each time we announce the next member of the sequence you must guess the finite set we chose.
Who wins: You win on a given sequence if all but finitely many of your guesses are right. You win the whole game if no matter which set we choose, and no matter what sequence we use to present it to you, you win on that sequence. Otherwise, we win.
It is clear how to win this game; just conjecture the finite set...
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Blum, L., & Blum, M. (1975). Toward a mathematical theory of inductive inference. Information and Control, 28, 125–155.
Gold, E. M. (1967). Language identification in the limit. Information and Control, 10, 447–474.
Jain, S., Osherson, D. N., Royer, J. S., & Sharma, A. (1999). Systems that learn: An introduction to learning theory (2nd ed.). Cambridge, MA: MIT Press.
Kelly, K. (1996). The logic of reliable inquiry. Oxford: Oxford University Press.
Martin, E., & Osherson, D. N. (1998). Belief revision in the service of scientific discovery. Mathematical Social Sciences, 36, 57–68.
Osherson, D., & Weinstein, S. (2008). Recognizing strong random reals. Review of Symbolic Logic, 1(1), 56–63.
Putnam, H. (1979). ‘Degree of confirmation’ and inductive logic. In Mathematics, matter, and method: Philosophical papers (2nd ed., Vol. I). New York: Cambridge University Press.
Shapiro, E. (1983). Algorithmic program debugging. Cambridge, MA: MIT Press.
Wexler, K., & Culicover, P. W. (1980). Formal principles of language acquisition. Cambridge, MA: MIT Press.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer Science+Business Media, LLC
About this entry
Cite this entry
Osherson, D., Weinstein, S. (2012). Formal Learning Theory. In: Seel, N.M. (eds) Encyclopedia of the Sciences of Learning. Springer, Boston, MA. https://doi.org/10.1007/978-1-4419-1428-6_444
Download citation
DOI: https://doi.org/10.1007/978-1-4419-1428-6_444
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4419-1427-9
Online ISBN: 978-1-4419-1428-6
eBook Packages: Humanities, Social Sciences and Law