7 citations · 12 across the 7 of their papers we have counts for
6 papers · 1 filter
Non-distributive positive logic as a fragment of first-order logic over semilattices
Jim de Groot
We characterise non-distributive positive logic as the fragment of a single-sorted first-order language that is preserved by a new notion of simulation called a meet-simulation. Me…
Positive Modal Logic Beyond Distributivity
Nick Bezhanishvili, Anna Dmitrieva, Jim de Groot +1
We develop a duality for (modal) lattices that need not be distributive, and use it to study positive (modal) logic beyond distributivity, which we call weak positive (modal) logic…
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…
Modal meet-implication logic
Jim de Groot, Dirk Pattinson
We extend the meet-implication fragment of propositional intuitionistic logic with a meet-preserving modality. We give semantics based on semilattices and a duality result with a s…
Goldblatt-Thomason Theorems for Modal Intuitionistic Logics
Jim de Groot
We prove a Goldblatt-Thomason theorem for dialgebraic intuitionistic logics, and instantiate it to Goldblatt-Thomason theorems for a wide variety of modal intuitionistic logics fro…
Coalgebraic Geometric Logic: Basic Theory
Nick Bezhanishvili, Jim de Groot, Yde Venema
Using the theory of coalgebra, we introduce a uniform framework for adding modalities to the language of propositional geometric logic. Models for this logic are based on coalgebra…