Inductive inference as ampliative and non monotonic reasoning
Isaac Levi · 2005
Inductive Inference is reasoning that justifies change from one state of full belief or absolute certainty to another by adding new information to the initial state that is consistent with it but does not entail it. Inductive inference is, therefore, ampliative. It is also non monotonic. But the deviations from monotonicity differ from those characterized by belief revision according to Alchourrón, Gärdenfors and Makinson or preferential entailment developed by Kraus, Lehmann and Magidor and Lehmann and Magidor. The default reasoning of Reiter resembles ampliative reasoning more closely according to the decision theoretic account of inductive expansion proposed in this essay. The paper seeks to explain the differences and why they occur. Induction and Abduction: Inductive inference is a species of justification. What is to be justified is an expansion of the current state of full belief K representable by a deductively closed theory or corpus K in a given language L by adding some specific item of information h to K and forming the deductive closure. The result is a new state of full belief. The reasoning involved in the justification shows, so I maintain, that the expansion by adding h is a best option given the goals of the inquiry in which the deliberation about