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

Ricardo Sousa Silvestre

doi:10.12775/LLP.2013.006

Authors

Ricardo Sousa Silvestre Federal University of Campina Grande

DOI:

https://doi.org/10.12775/LLP.2013.006

Keywords

paraconsistent logic, paracomplete logic, modal logic, inductive plausibility

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.

Author Biography

Ricardo Sousa Silvestre, Federal University of Campina Grande

Department of Philosophy

References

Chellas, B., Modal Logic: An Introduction, Cambridge University Press, Cambridge, 1980.

Fitting, M., “Basic modal logic”, pages 368-448 in Handbook of Logic in Artificial Intelligence and Logic Programming}, vol. 1, “Logical Foundations”, D. Gabbay, D. Hogger, and J. Robinson (eds.), Oxford University Press, Oxford, 1993.

Hughes, G., and M. Cresswell, A New Introduction to Modal Logic, Routledge, New York, 1996.

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.