Compact models for multi-modal logics

We propose a new representation formalism for the multimodal logic Km, in which labels replace modalities in all formulas and subformulas: Possibility operators are represented by constants and necessity operators by anonymous variables. Our formalism gives rise to a new definition of models which can be much more compactly represented than traditional Kripke models. We describe how a Km formula is converted into labelled form; we then give a decision procedure for labelled formulas which returns a model exactly when the formulas are satisfiable. Furthermore, we explain how a Kripke model for the original Km formula can be derived from a labelled model.