Multi-Dimensional Modal Logic

We start with informally defining the subject matter of this book: multi-dimensional modal logic (MDML). First let us briefly consider what we understand by the notion of “modal logic”. The last decade has seen a development in modal logic towards a more abstract and technical approach. In this perspective of what one might call abstract modal logic, arbitrary relational structures can be seen as models for an (extended) modal language: any relation is a potential accessibility relation of some suitably defined modal operator. As the essentially modal aspect of the framework one could point out that the mechanism for evaluating formulas forces certain moves along the accessibility relations. Thus, for instance quantification over a model is restricted to an “accessible” part of the structure.