Combining Monotone and Normal Modal Logic in Nested Sequents – with Countermodels

Abstract

We introduce nested sequent calculi for bimodal monotone modal logic, aka. Brown’s ability logic, a natural combination of non-normal monotone modal logic M and normal modal logic K. The calculus generalises in a natural way previously existing calculi for both mentioned logics, has syntactical cut elimination, and can be used to construct countermodels in the neighbourhood semantics. We then consider some extensions of interest for deontic logic. An implementation is also available.