The logic of generality

One hypothesis is more general than another one if it covers all instances that are also covered by the later one. The former hypothesis is called a generalization of the later, and the later a specialization of the former. When using logical formulae as hypotheses, the generality relation coincides with the notion of logical entailment, which implies that the generality relation can be analyzed from a logical perspective. The logical analysis of generality, which is pursued in this entry, leads to the perspective of induction as the inverse of deduction. This forms the basis for an analysis of various logical frameworks for reasoning about generality and for traversing the space of possible hypotheses. Many of these frameworks (such as for instance, θ-subsumption) are employed in the field inductive logic programming and are introduced below.