Logic and Learning

The theory of first-order logic - or "Model Theory" - appears in few studies of learning and scientific discovery. We speculate about the reasons for this omission, and then argue for the utility of Model Theory in the analysis and design of automated systems of scientific discovery. One scientific task is treated from this perspective in detail, namely, concept discovery. Two formal paradigms bearing on this probleni are presented and investigated using the tools of logical theory. One paradigm bears on PAC learning, the other on identification in the limit.