A Unified Interpretation of the Semantics of Relevance Logic

Mind 132 (528) (2023)
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Abstract

I introduce a novel and quite intuitive interpretation of the ternary relation that figures in the relational semantics of many relevance logics. Conceptually, my interpretation makes use only of incompatibility and parthood relations, defined over a set of states. In this way, the proposed interpretation—of the ternary relation and the conditional—extends Dunn’s and Restall’s works on negation and the Routley star operator. Therefore, the interpretation is unified, and hence not only intuitive but also parsimonious. Additionally, the interpretation provides us with a cogent argument to the effect that a ternary relation is indispensable, and we cannot merely do with a binary relation.

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Rea Golan
Ben-Gurion University of the Negev

Citations of this work

Why Must Incompatibility Be Symmetric?Ryan Simonelli - 2024 - Philosophical Quarterly 74 (2):658-682.

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References found in this work

Negation on the Australian Plan.Francesco Berto & Greg Restall - 2019 - Journal of Philosophical Logic 48 (6):1119-1144.
The Law of Non-Contradiction as a Metaphysical Principle.Tuomas E. Tahko - 2009 - Australasian Journal of Logic 7:32-47.
A Modality Called ‘Negation’.Francesco Berto - 2015 - Mind 124 (495):761-793.
Impossible Worlds.Mark Jago - 2013 - Noûs 47 (3):713-728.
Star and perp: Two treatments of negation.J. Michael Dunn - 1993 - Philosophical Perspectives 7:331-357.

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