Speaker
Sabine Frittella
(Aix-Marseille Université)

Abstract
(joint work with Giuseppe Greco)
Monotone modal logic is a weaker version of normal modal logic, where modalities are monotone but do not distribute over either joins or meets.
In this talk I will explain why the proof theory for these logics is still unsatisfactory and I will argue that a display-style calculus for monotone modal logic would be adequate.
I will show that a naive design for such a calculus runs into technical difficulties.
Finally I will present a generalization of display calculi that does not automatically force modal operators to be adjoints, and I will explain why it can be considered adequate from a proof-theoretical perspective.