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## Towards a Display-style Calculus for Monotone Modal Logic

### March 10, 2014 @ 2:30 pm - 3:00 pm

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**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.