On 16 Jun 2011, at 18:36, meekerdb wrote:

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On 6/16/2011 7:38 AM, Bruno Marchal wrote:Concerning the learning competence of a machine, I measure it bythe classes of computable functions that the machine is able toidentify from finite samples of input-outputs. This leads to the"computational learning theory" or "inductive inference" theory,which shows that the possible competences form a complex latticewith a lot of incomparable competences, and with a lot ofnecessarily non constructive gaps existing among them.Do you have some reference where this is explained?

My favorite paper on this is:

`CASE J. & SMITH C., 1983, Comparison of Identification Criteria for`

`Machine Inductive`

Inference. In Theoretical Computer Science 25,.pp 193-220.

`But since, there has been a ton of papers published. Notably the COLT`

`proceedings.`

There is also the book:

`OSHERSON D.N., STOB M.and WEINSTEIN S., 1986, Systems that Learn, MIT`

`press. (New edition exists since)`

`It is a recursion theoretic based field. Of course it does not`

`interest so much the engineers as most result are not constructive,`

`indeed necessarily so.`

A basic fundamental paper is:

`GOLD, E. M., 1965, Limiting recursion, Journal of Symbolic Logic, 30,`

`1, pp. 27-48.`

and

`GOLD E.M., 1967, Language Identification in the Limit. Information &`

`Control 10, pp.`

447-474. Another one is:

`BLUM L. & BLUM M., 1975, Toward a Mathematical Theory of Inductive`

`Inference.`

Information and Control 28,.pp. 125-155.

`There is a full chapter on this in "Conscience et mécanisme". You will`

`find other references in the "bibilographie générale" pdf.`

http://iridia.ulb.ac.be/~marchal/bxlthesis/consciencemecanisme.html

`The gap G* minus G formalizes an easy set of inferable but non`

`provable self-referential truth by inductive inference type of Löbian`

`machines (the 'mystical machines').`

Bruno http://iridia.ulb.ac.be/~marchal/ -- You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to everything-list@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.