8 papers · 1 filter
Intuitionistic K is a Bisimulation-Invariant Fragment of Intuitionistic First-Order Logic
Jim de Groot, João Marcos, Rodrigo Stefanes
We define the notion of IK-bisimulation between the relational semantics for the intuitionistic modal logic IK, and prove that IK arises as the IK-bisimulation-invariant fragment o…
Modal Measurable Logics via a Modal Loomis-Sikorski Representation Theorem
Nick Bezhanishvili, Jim de Groot, Lawrence S. Moss
We investigate a modal extension of the infinitary classical logic with countable meets and joins, formulated with an eye toward measure-theoretic work in dynamical systems and in…
Relational Semantics for Flat Heyting-Lewis Logic
Jim de Groot, Tadeusz Litak
We introduce relational semantics for "flat Heyting-Lewis logic" HLC-flat. This logic arises as the extension of intuitionistic logic with a Lewis-style strict implication modality…
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…
Filling in the semantics for intuitionistic conditional logic
Brendan Dufty, Jim de Groot
We prove completeness results for a wide variety of intuitionistic conditional logics. We do so by first using a canonical model construction obtain completeness with respect to de…
Gödel-McKinsey-Tarski and (not quite) Blok-Esakia for Heyting-Lewis Implication
Jim de Groot, Tadeusz Litak, Dirk Pattinson
Heyting-Lewis Logic is the extension of intuitionistic propositional logic with a strict implication connective that satisfies the constructive counterparts of axioms for strict im…