Induction and plausibility: A formal approach from the standpoint of artificial intelligence

The purpose of this work is to analyze the notion of induction, conceived as the class of rational non-truth preserving inferences, from the point of view of the nonmonotonic logical tradition raised inside the field of Artificial Intelligence (AI) in the last twenty-five years. By centering our efforts around what has been called the problem of description of induction, we intend to explicate (in Carnap's sense) the notion of induction through a purely descriptive and consequently justificatory-free approach to induction. Of fundamental importance for this enterprise is the notion of plausibility, here understood as the same as Carnap's notion of pragmatical probability. By providing a representational formal analysis of the notion of induction, we also aim to explicate something akin to the ordinary notion of plausibility. One of the main features of this relationship between induction and plausibility concerns the two most basic approaches one can take when dealing with the contradictions that are sure to arise from the use of inductive inferences. These skeptical and credulous approaches to induction, as we have named them, give rise to two different plausibility notions which bear important relations to a domain of formal logic closely connected with AI, the field of paraconsistent and paracomplete logic: while the skeptical plausibility is a paracomplete notion, the credulous plausibility is a paraconsistent one. At the basis of our formal work is the result that in opposition to the formal approaches developed in philosophy, the justificatory-free aspect we are looking for is already present in most nonmonotonic logics. We pick two of these formalisms---Reiter's default logic and Pequeno's paraconsistent default logics---and extend them in such a way as to obtain a system able to perform the task a descriptive logic of induction is supposed to perform. To complete our formal work, we also develop a so-called paranormal (i.e., simultaneously paracomplete and paraconsistent) modal logic to represent the two notions of plausibility and act in conjunction with the mentioned nonmonotonic logic. In this way, our work is also a contribution to the field of modal logic. In order to show the applicability of our system, we present a formalization of the so-called abductive reasoning and hypothetico-deductive reasoning applied to the problem of confirmation of hypotheses in philosophy of science.