Abstract
There is a small family of many-valued logics associated with the logic of First Degree Entailment. These may be called the FDE family. The purpose of the present paper is to provide natural deduction systems for these logics. This can be done in a quite systematic fashion. An appendix to the paper deals with a closely related system which is not in the family, “Paraconsistent Weak Kleene”.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Bonzo, S., Gil-Férez, J., Paoli, F. (2017), ‘On Paraconsistent Weak Kleene Logic’, Studia Logica 105: 253–98.
Ciuni, R., and Carrara, M. (2016), ‘Characterizing Logical Consequence in Paraconsistent Weak Kleene’, pp. 165–176 of L. Felline, F. Paoli, and E. Rossanese (eds.), New Developments in Logic and Philosophy of Science, London: College Publications.
Daniels., D. (1990), ‘A Note on Negation’, Erkenntnis 32: 423–9.
Goddard, L. and Routley, R. (1973) The Logic of Significance and Context, New York, NY: Halsted Press.
Haack, S. (1996), Deviant Logic, Fuzzy Logic: Beyond the Formalism, Chicago, IL: University of Chicago Press.
Halldén, S. (1949) The Logic of Nonsense, Uppsala: Lundequista Bokhandeln
Oller, C. (1999), ‘Paraconsistency and Analyticity’, Logic and Logical Philosophy 7: 91–9.
Prawitz, D. (1965), Natural Deduction: a Proof-Theoretical Study, Stockholm: Almqvist & Wiksell.
Priest, G. (2008), Introduction to Non-Classical Logics: From If to Is, Cambridge: Cambridge University Press.
Priest, G. (2010), ‘The Logic of the Catuṣkoṭi’, Comparative Philosophy 1: 32–54.
Priest, G. (2014a), ‘Speaking of the Ineffable…’, ch. 7 of J. Lee and D. Berger (eds.), Nothingness in Asian Philosophy, London: Routledge.
Priest, G. (2014b), ‘Plurivalent Logic’, Australasian Journal of Logic 11, article 1. http://ojs.victoria.ac.nz/ajl/article/view/1830.
Prior, A., (1957), Time and Modality, Oxford: Oxford University Press.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2019 Springer Nature Switzerland AG
About this chapter
Cite this chapter
Priest, G. (2019). Natural Deduction Systems for Logics in the FDE Family. In: Omori, H., Wansing, H. (eds) New Essays on Belnap-Dunn Logic. Synthese Library, vol 418. Springer, Cham. https://doi.org/10.1007/978-3-030-31136-0_16
Download citation
DOI: https://doi.org/10.1007/978-3-030-31136-0_16
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-31135-3
Online ISBN: 978-3-030-31136-0
eBook Packages: Religion and PhilosophyPhilosophy and Religion (R0)