--- The best sourse on the inferential theory is probably my chapter "Inferential Theory of Learning: Developing Foundations for Multistrategy Learning" in Machine Learning: A Multistrategy Approach, Morgan Kaufman Publishers, 1994.>>I would like to respond to one of the above points, namely that induction is falsity-preserving. This has always struck me as something odd: why is falsity worth preserving? In my PhD thesis I have proposed an alternative view: explanatory induction is a form of induction that preserves (amplifies) explanatory power from premises to inductive hypothesis. Of course, if we identify explanatory power with deductive closure, then the two views coincide. However, the explanatory view has the merit that it is expressed in terms of something worth preserving.
--- The importance of "falsity preserving" of induction is that its results entail (jointly with BK) the observations (inputs to induction); thus reasoning from the hypotheses to the facts ("consequents") is truth-preserving. This property characterizes all forms of induction (such as inductive generalization, inductive specialization, abduction, inductive concretion, etc.). Hope this helps a little. Details (and a more precise elaboration of the above) are in the paper listed above.Ryszard