ModalLogic

Ordinary logic asks whether a statement holds. Modal logic asks how it holds: necessarily, or only as things happen to be; at every later moment, or merely at some; after every run of a program, or after one.

The extra reading is given by relating one way things might be to another, and a modal statement is then read across that relation rather than at a single point. Which principles come out valid depends on what is assumed about the relation, so the subject is less one logic than a family of them.