Authors
Jeremy Seligman
University of Auckland
Jc Beall
University of Notre Dame
Abstract
We shed light on an old problem by showing that the logic LP cannot define a binary connective $\odot$ obeying detachment in the sense that every valuation satisfying $\varphi$ and $(\varphi\odot\psi)$ also satisfies $\psi$ , except trivially. We derive this as a corollary of a more general result concerning variable sharing
Keywords LP   detachment-free logics   detachable connective   paradox   relevance logics   variable-sharing   paraconsistent logic
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DOI 10.1215/00294527-1731353
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References found in this work BETA

The Logic of Paradox.Graham Priest - 1979 - Journal of Philosophical Logic 8 (1):219 - 241.
A Useful Four-Valued Logic.N. D. Belnap - 1977 - In J. M. Dunn & G. Epstein (eds.), Modern Uses of Multiple-Valued Logic. D. Reidel.
Logic for Equivocators.David Lewis - 1982 - Noûs 16 (3):431-441.
A Calculus for Antinomies.F. G. Asenjo - 1966 - Notre Dame Journal of Formal Logic 16 (1):103-105.
Multiple-Conclusion Lp and Default Classicality.Jc Beall - 2011 - Review of Symbolic Logic 4 (2):326-336.

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Citations of this work BETA

What Is an Inconsistent Truth Table?Zach Weber, Guillermo Badia & Patrick Girard - 2016 - Australasian Journal of Philosophy 94 (3):533-548.
Paraconsistent Dynamics.Patrick Girard & Koji Tanaka - 2016 - Synthese 193 (1):1-14.

View all 15 citations / Add more citations

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