In Marcin Trepczyński (ed.), Philosophical Approaches to the Foundations of Logics and Mathematics. Leiden, Países Baixos: pp. 193-210 (2021)

Authors
Ricardo Silvestre
Federal University of Campina Grande
Abstract
Is it possible to combine different logics into a coherent system with the goal of applying it to specific problems so that it sheds some light on foundational aspects of those logics? These are two of the most basic issues of combining logics. Paranormal modal logic is a combination of paraconsistent logic and modal logic. In this paper, I propose two further combinatory developments, focusing on each one of these two issues. On the foundational side, I combine paranormal modal logic with normal modal logic, resulting into a paraconsistent and paracomplete multimodal logic dealing with the notions of plausibility and certainty. On the application side, I combine this logic with Reiter’s default logic, resulting into an inductive and consequently nonmonotonic paraconsistent and paracomplete logic able to represent some key inductive principles.
Keywords paranormal modal logic   multimodal logic  Reiter default logic  Carnap’s pragmatical probability
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