Propositional Linear Temporal Logic, also known as Propositional Linear Time Logic has the natural number
line ordered by < as the intended model. It is used to model temporal behaviour with two basic modal
operators X p interpreted as "the next state makes p true" and p Un q interpreted as "p is true from now
until q becomes true". The other operators are defined from these.
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.