Abstract: Multimodal logic concerns with the study of logic that contain a variety of modalities. The systems of multimodal logic contain two or more unreducible modal operators. The study of multimodal logic can provide a unified formal framework for the study of many types of modalities. The basic theory of multimodal logic is an important part of modal logic. The multimodal operator and its representation, the research perspective of multimodal logic, the separability of multimodal logic systems, and the choice of semantics of multimodal logic are basic issues in the study of the basic theory of multimodal logic. The clarification and resolution of these issues will help the further development of multimodal logic.

Key words: multimodal, modal operator, axiom schema, separability, semantics