MODAL LOGIC WITHOUT CONTRACTION IN A METATHEORY WITHOUT CONTRACTION
Patrick Girard, Zach Weber · The Review of Symbolic Logic · 2019
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.