Often known as Branching Time Temporal Logic, CTL allows us to state properties which may be true

on all paths or on some paths in a rooted tree where each branch is a copy of the natural numbers.

For an introduction to temporal logics, see

http://plato.stanford.edu/entries/logic-temporal/

When you enter a formula A, then "closed" means that A is a

theorem because the tableau for ~ A is closed, and "open" means

that it is not a theorem because the tableau for ~ A is open.

When you enter a formula A, then "closed" means that A is a

theorem because the tableau for ~ A is closed, and "open" means

that it is not a theorem because the tableau for ~ A is open.