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.