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

• Authors: Ricardo S. Silvestre
• Languages of publication: EN

Abstracts

EN

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

EN

paraconsistent logic; paracomplete logic; modal logic; inductive plausibility

• Publisher: Uniwersytet Mikołaja Kopernika (Nicolaus Copernicus University in Toruń)
• Journal: Logic and Logical Philosophy
• Year: 2013
• Volume: 22
• Issue: 1
• Pages: 89-130

Dates

published

2013-03-01

online

2013-07-02

Contributors

author

Ricardo S. Silvestre

• Department of Philosophy Federal University of Campina Grande Rua Aprígio Veloso 882 Campina Grande-PB, Brazil, 58429-900 [phone]

References

• [1] Chellas, B., Modal Logic: An Introduction, Cambridge University Press, Cambridge, 1980.
• [2] Fitting, M., “Basic modal logic”, pages 368-448 in Handbook of Logic inArtificial Intelligence and Logic Programming, vol. 1, “Logical Founda- tions”, D. Gabbay, D. Hogger, and J. Robinson (eds.), Oxford University Press, Oxford, 1993.
• [3] Hughes, G., and M. Cresswell, A New Introduction to Modal Logic, Rout- ledge, New York, 1996.
• [4] Silvestre, R. S., “Paranormal modal logic - Part I: The system K? and the foundations of the Logic of skeptical and credulous plausibility”, Logicand Logical Philosophy 21, 1 (2012): 65-96. DOI: 10.12775/LLP.2012.005[Crossref]
• [5] Silvestre, R. S., Induction and Plausibility. A Conceptual Analysis fromthe Standpoint of Nonmonotonicity, Paraconsistency and Modal Logic, Lambert Academic Publishing, Saarbrucken, 2010.
• [6] 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.

Identifiers

DOI

10.12775/LLP.2013.006