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Semantical Analysis of Intuitionistic Modal Logics between CK and IK
Jim de Groot, Ian Shillito, Ranald Clouston
The intuitionistic modal logics considered between Constructive K (CK) and Intuitionistic K (IK) differ in their treatment of the possibility (diamond) connective. It was recently…
Taking Bi-Intuitionistic Logic First-Order: A Proof-Theoretic Investigation via Polytree Sequents
Tim S. Lyon, Ian Shillito, Alwen Tiu
It is well-known that extending the Hilbert axiomatic system for first-order intuitionistic logic with an exclusion operator, that is dual to implication, collapses the domains of…
Mechanised uniform interpolation for modal logics K, GL, and iSL
Hugo Férée, Iris van der Giessen, Sam van Gool +1
The uniform interpolation property in a given logic can be understood as the definability of propositional quantifiers. We mechanise the computation of these quantifiers and prove…