Model Theoretical Aspects of Weakly Aggregative Modal Logic

Weakly Aggregative Modal Logic ) is a collection of disguised polyadic modal logics with n-ary modalities whose arguments are all the same. \ has interesting applications on epistemic logic, deontic logic, and the logic of belief. In this paper, we study some basic model theoretical aspects of \. Specifically, we first give a van Benthem–Rosen characterization theorem of \ based on an intuitive notion of bisimulation. Then, in contrast to many well known normal or non-normal modal logics, we show that each basic \ system \ lacks Craig interpolation. Finally, by model theoretical techniques, we show that an extension of \ does have Craig interpolation, as an example of amending the interpolation problem of \.