Modal logic is an extension of ordinary propositional logic. Its purpose is to model our reasoning about statements that do not correspond to actual facts in the world. In general, the goal of logic is to formalize the structure of human reasoning. With a standardized abstract language of thought we hope to communicate facts about the world efficiently and accurately. Propositional logic and its extensions, first and second order logic, are meant to resolve questions about how the world is, e.g., "is the sum of the angles of a triangle 180 degrees?"

However, we do not always contemplate the way the world is. Often we think and argue about how the world might or should be. Could the South have won the Civil War? Should we feed the starving of the world? The answers to these questions are not statements about how the world actually is...