Review of Symbolic Logic:1-38 (forthcoming)

Authors
Greg Restall
University of Melbourne
Shawn Standefer
National Taiwan University
Abstract
We present a new frame semantics for positive relevant and substructural propositional logics. This frame semantics is both a generalisation of Routley–Meyer ternary frames and a simplification of them. The key innovation of this semantics is the use of a single accessibility relation to relate collections of points to points. Different logics are modeled by varying the kinds of collections used: they can be sets, multisets, lists or trees. We show that collection frames on trees are sound and complete for the basic positive distributive substructural logic $\mathsf {B}^+$, that collection frames on multisets are sound and complete for $\mathsf {RW}^+$, and that collection frames on sets are sound for the positive relevant logic $\mathsf {R}^+$. The completeness of set frames for $\mathsf {R}^+$ is, currently, an open question.
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DOI 10.1017/s1755020322000272
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References found in this work BETA

Logical Pluralism.Jc Beall & Greg Restall - 2000 - Australasian Journal of Philosophy 78 (4):475 – 493.
Structural Reflexivity and the Paradoxes of Self-Reference.Rohan French - 2016 - Ergo: An Open Access Journal of Philosophy 3.
The Mathematics of Sentence Structure.Joachim Lambek - 1958 - Journal of Symbolic Logic 65 (3):154-170.

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