Modal Logic Without Contraction in a Metatheory Without Contraction

Review of Symbolic Logic 12 (4):685-701 (2019)
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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 anonclassical substructural logicas 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 anoncontractive logicin the background. This sheds light on which modal principles are invariant under changes of metalogic, and provides (further) evidence for the general viability of nonclassical mathematics.

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Author's Profile

Patrick Girard
University of Auckland

Citations of this work

Observations on the Trivial World.Zach Weber & Hitoshi Omori - 2019 - Erkenntnis 84 (5):975-994.
Semantics without Toil? Brady and Rush Meet Halldén.Lloyd Humberstone - 2019 - Organon F: Medzinárodný Časopis Pre Analytickú Filozofiu 26 (3):340–404.
Preface.Matteo Pascucci & Adam Tamas Tuboly - 2019 - Organon F: Medzinárodný Časopis Pre Analytickú Filozofiu 26 (3):318-322.

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References found in this work

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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