Formal Learning Theory in Context

One version of the problem of induction is how to justify hypotheses in the face of data. Why advance hypothesis A rather than B — or in a probabilistic context, why attach greater probability to A than B? If the data arrive as a stream of observations (distributed through time) then the problem is to justify the associated stream of hypotheses. Several perspectives on this problem have been developed including Bayesianism [Howson and Urbach, 1993] and belief-updating [Hansson, 1999]. These are broad families of approaches; the citations are meant just as portals. Another approach is to attempt to justify the present choice of hypothesis by situating it in a strategy with good long-term prospects. Such is the idea behind Formal Learning Theory, which will be discussed in what follows. We’ll see that it is naturally grouped with the somewhat older concept of a confidence interval.