Most of my life I've lived in Amsterdam. I studied maths at the University of Amsterdam. After my master's there I moved to Australia to do a PhD under the supervision of Dirk Pattinson.
Roughly, I am interested in categorical dualities in logic. Here are some more specific questions I sometimes think about.
- In our recent paper Dirk and I proposed the idea of dialgebraic logic, which provide a coalgebra-like framework for modal logics. All examples we gave are modal extensions of intuitionistic logics. I'm wondering if there are more logical paradigms that fit the framework of dialgebraic logic.
- Yosida duality is a duality for compact Hausdorff spaces with certain Riesz spaces. I'm curious if there is a natural description of the Yosida dual of the Vietoris functor and whether this gives rise to an interesting modal logic. (The Vietoris functor is of course well-known from its appearance in modal logic over a classical base.)
- More to come
- Coalgebraic Geometric Logic: Basic Theory
Nick Bezhanishvili, Jim de Groot & Yde Venema, Submitted March 2020
- Logic-Induced Bisimulations (report version with proofs)
Jim de Groot, Helle Hvid Hansen & Alexander Kurz, to appear at AiML 2020
- Modal Intuitionistic Logics as Dialgebraic Logics (pdf, video)
Jim de Groot & Dirk Pattinson, LICS 2020
- Duality for Instantial Neighbourhood Logic via Coalgebra (pdf)
Nick Bezhanishvili, Sebastian Enqvist & Jim de Groot, CMCS 2020
- Hennessy-Milner Properties for (Modal) Bi-intuitionistic Logic
Jim de Groot & Dirk Pattinson, WoLLIC 2019
- Coalgebraic Geometric Logic
Nick Bezhanishvili, Jim de Groot & Yde Venema, CALCO 2019