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 𝕂_n lacks Craig interpolation. Finally, by model theoretical techniques, we show that an extension of 𝕂_2 does have Craig interpolation, as an example of amending the interpolation problem of .