Four-valued semantics for relevant logics (and some of their rivals)

Journal of Philosophical Logic 24 (2):139 - 160 (1995)

Authors
Greg Restall
University of Melbourne
Abstract
This paper gives an outline of three different approaches to the four-valued semantics for relevant logics (and other non-classical logics in their vicinity). The first approach borrows from the 'Australian Plan' semantics, which uses a unary operator '⋆' for the evaluation of negation. This approach can model anything that the two-valued account can, but at the cost of relying on insights from the Australian Plan. The second approach is natural, well motivated, independent of the Australian Plan, and it provides a semantics for the contraction-free relevant logic C (or RW). Unfortunately, its approach seems to model little else. The third approach seems to capture a wide range of formal systems, but at the time of writing, lacks a completeness proof
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DOI 10.1007/BF01048529
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References found in this work BETA

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 of Paradox.Graham Priest - 1979 - Journal of Philosophical Logic 8 (1):219-241.

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Citations of this work BETA

Relevant Restricted Quantification.J. C. Beall, Ross T. Brady, A. P. Hazen, Graham Priest & Greg Restall - 2006 - Journal of Philosophical Logic 35 (6):587-598.
HYPE: A System of Hyperintensional Logic.Hannes Leitgeb - 2019 - Journal of Philosophical Logic 48 (2):305-405.
Algebraic Kripke-Style Semantics for Relevance Logics.Eunsuk Yang - 2014 - Journal of Philosophical Logic 43 (4):803-826.
Notes on Stratified Semantics.Shay Allen Logan - forthcoming - Journal of Philosophical Logic:1-38.

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