Review of Symbolic Logic 12 (4):685-701 (2019)

Authors
Patrick Girard
University of Auckland
Abstract
Standard reasoning about Kripke semantics for modal logic is almost always based on a background framework of classical logic. Can proofs for familiar definability theorems be carried out using a nonclassical substructural logic as the metatheory? This article presents a semantics for positive substructural modal logic and studies the connection between frame conditions and formulas, via definability theorems. The novelty is that all the proofs are carried out with a noncontractive logic in the background. This sheds light on which modal principles are invariant under changes of metalogic, and provides evidence for the general viability of nonclassical mathematics.
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DOI 10.1017/s1755020319000030
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References found in this work BETA

Toward Useful Type-Free Theories. I.Solomon Feferman - 1984 - Journal of Symbolic Logic 49 (1):75-111.
Logics Without the Contraction Rule.Hiroakira Ono & Yuichi Komori - 1985 - Journal of Symbolic Logic 50 (1):169-201.
What Is an Inconsistent Truth Table?Zach Weber, Guillermo Badia & Patrick Girard - 2016 - Australasian Journal of Philosophy 94 (3):533-548.
Kripke Models for Linear Logic.Gerard Allwein & J. Michael Dunn - 1993 - Journal of Symbolic Logic 58 (2):514-545.

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Citations of this work BETA

Observations on the Trivial World.Zach Weber & Hitoshi Omori - 2019 - Erkenntnis 84 (5):975-994.
Preface.Matteo Pascucci & Adam Tamas Tuboly - 2019 - Organon F: Medzinárodný Časopis Pre Analytickú Filozofiu 26 (3):318-322.

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