Research

I'm a mathematician turned logician, and I currently work on non-classical modal logic.

Non-distributive logics

(More details soon)

Intuitionistic modal logics

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Duality theory

Categorical dualities between the algebraic semantics and the frame semantics (with extra structure) of a logic allow one to move between these two perspectives. This allows us to prove properties about our logic using whatever perspective is easier. I like using topology (as extra structure) to obtain such dualities for modal and non-classical logics.

Bisimulations

Bisimulations between models are structures that allow you to say that two states satisfy precisely the same formulae without checking this for all formulae individually. Furthermore, bisimulations often link modal logics with first-order logic, as modal logics can be described as the bisimulation-invariant fragment of (suitable chosen) first-order logics. While bisimulations for normal modal logic have been well researched, there are still many questions about bisimulations for non-normal and non-classical modal logics.

Coalgebraic and dialgebraic logic

Coalgebraic and dialgebraic logics provide general frameworks for studying a wide array of logics. The purpose of this framework is to allow for general theorems, and thus to prevent the need to prove properties for each logic individually. Dialgebraic logic was born from the desire of a coalgebra-like framework that captures modal extensions of intuitionistic logic, and has already proven fruitful to obtain, for example, a general Goldblatt-Thomason style theorem for them. More generally, I am interested in non-classical logics with odd semantics.