About

While formal logic is the mathematical study of general valid reasoning, Modal Logic is a sub-field that focuses on modal languages that approach reasoning tasks in terms of striking a good balance between expressivity and computational tractability. Traditionally an expertise of Dutch logicians, nowadays modal logics are being applied to a wide variety of modelling tasks worldwide: from the representation of agents’ information and dispositions to the description of computational processes.

Category Theory is an influential framework that has been used in a wide variety of mathematical sub-disciplines, from set theory to geometry, to introduce generality at the right abstraction level. In particular, category theory has long had connections with mathematical logic and computation through proof theories and type theories, recent examples being co-algebra of infinite processes and the pre-sheaf approach in  concurrency theory. What is relatively new, however, are interactions with modal logic.

At this workshop, we will look into connections between the two fields, including current uses of category theory in the semantics of modal logics, ways of generalising modal logics to category-theoretic versions, and analysing new modal semantics of information flow and agency as developed in The Netherlands in category-theoretic terms. Conversely, notions and techniques from modal logic can be introduced into category theory, giving rise to new languages and new kinds of completeness and decidability proofs.