A Coalgebraic Perspective on Monotone Modal Logic
Helle Hvid Hansen, Clemens Kupke · Electronic Notes in Theoretical Computer Science · 2004
The paper has two main parts: First we make the connection between monotone modal logic and the general theory of coalgebras precise by defining functors UpP:Set→Set and UpV:Stone→Stone such that UpP- and UpV-coalgebras correspond to monotone neighbourhood frames and descriptive general monotone frames, respectively. Then we investigate the relationship between the coalgebraic notions of equivalence and monotone bisimulation. In particular, we show that the UpP-functor does not preserve weak pullbacks, and we prove interpolation for a number of monotone modal logics using results on UpP-bisimulations.