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Intuitionistic Justification Logic, Semantically
Sonia Marin, Paaras Padhiar, Ian Shillito
Justification logics are explicit versions of modal logic. In the classical setting, this means boxes are refined with explicit proof terms and interact with each other through pro…
Uniform interpolation with constructive diamond
Iris van der Giessen, Ian Shillito
Uniform interpolation is a strong form of interpolation providing an interpretation of propositional quantifiers within a propositional logic. Pitts' seminal work establishes this…
Pitts and Intuitionistic Multi-Succedent: Uniform Interpolation for KM
Hugo Férée, Ian Shillito
Pitts' proof-theoretic technique for uniform interpolation, which generates uniform interpolants from terminating sequent calculi, has only been applied to logics on an intuitionis…
Duality for Constructive Modal Logics: from Sahqlvist to Goldblatt-Thomason
Jim de Groot, Ian Shillito, Ranald Clouston
We carry out a semantic study of the constructive modal logic CK. We provide a categorical duality linking the algebraic and birelational semantics of the logic. We then use this t…