Logical Characterisations of Inductive Learning

This chapter presents a logical analysis of induction. Contrary to common approaches to inductive logic that treat inductive validity as a real-valued generalisation of deductive validity, we argue that the only logical step in induction lies in hypothesis generation rather than evaluation. Inspired by the seminal paper of Kraus, Lehmann and Magidor [Kraus et al., 1990] we analyse the logic of inductive hypothesis generation on the meta-level of consequence relations. Two main forms of induction are considered: explanatory induction, aimed at inducing a general theory explaining given observations, and confirmatory induction, aimed at characterising completely or partly observed models. Several sets of meta-theoretical properties of inductive consequence relations are considered, each of them characterised by a suitable semantics. The approach followed in this chapter is extensively motivated by referring to recent and older work in philosophy, logic, and machine learning.