Paranormal modal logic – Part II: K?, K and Classical Logic and other paranormal modal systems

Ricardo Sousa Silvestre

DOI: http://dx.doi.org/10.12775/LLP.2013.006

Abstract


In this two-part paper we present paranormal modal logic: a modal logic which is both paraconsistent and paracomplete. Besides using a general framework in which a wide range of logics – including normal modal logics, paranormal modal logics and classical logic – can be defined and proving some key theorems about paranormal modal logic (including that it is inferentially equivalent to classical normal modal logic), we also provide a philosophical justification for the view that paranormal modal logic is a formalization of the notions of skeptical and credulous plausibility.


Keywords


paraconsistent logic; paracomplete logic; modal logic; inductive plausibility

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References


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Silvestre, R. S., “Paranormal modal logic – Part I: The system K? and the foundations of the Logic of skeptical and credulous plausibility”, Logic and Logical Philosophy 21, 1 (2012): 65-96. DOI: 10.12775/LLP.2012.005

Silvestre, R. S., Induction and Plausibility. A Conceptual Analysis from the Standpoint of Nonmonotonicity, Paraconsistency and Modal Logic, Lambert Academic Publishing, Saarbrucken, 2010.

Silvestre, R. S., “Modality, paraconsistency and paracompleteness”, pages 449-467 in Advances in Modal Logic, vol. 6, G. Governatori, I. Hodkinson and Y. Venema (eds.), Noosa, College Publications, 2006.








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