Combining Inductive Generalization and Factual Abduction

The aim of this paper is to outline a first-order model for ampliative reasoning that fruitfully combines the inference patterns of inductive generalization and factual abduction. The pattern of inductive generalization is the archetype pattern of inductive inference by which we arrive at a universally quantified statement (All P s are Q) given one or more instances (Some P s are Q). In factual abduction, we reason from a universally quantified statement (All P s are Q) and an instance of its consequent (object a is Q) to an instance of its antecedent (object a is P ). It is shown how these patterns can be combined in such a way that inductively inferred generalizations can be used as premises in abductive inferences, and that conclusions of abductive inferences in turn can be used to inductively infer new generalizations. This process is formally explicated within the adaptive logics framework in terms of a preferential model semantics.