The Free On-line Dictionary of Computing (30 December 2018):

temporal logic

    An extension of predicate calculus which includes
   notation for arguing about *when* statements are true.  Time
   is discrete and extends indefinitely into the future.  Three
   prefix operators, represented by a circle, square and diamond
   mean "is true at the next time instant", "is true from now on"
   and "is eventually true".  x U y means x is true until y is
   true.  x P y means x precedes y.

   There are two types of formula: "state formulae" about things
   true at one point in time, and "path formulae" about things
   true for a sequence of steps.  An example of a path formula is
   "x U y", and example of a state formula is "next x" or a
   simple atomic formula such at "waiting".

   "true until" in this context means that a state formula holds
   at every point in time up to a point when another formula
   holds.  "x U y" is the "strong until" and implies that there
   is a time when y is true.  "x W y" is the "weak until" in
   which it is not necessary that y holds eventually.

   There are two types of temporal logic used: branching time and
   linear time.  The basic propositional temporal logic cannot
   differentiate between the two, though.  Linear time considers
   only one possible future, in branching time you have several
   alternative futures.  In branching temporal logic you have the
   extra operators "A" (for "all futures") and "E" (for "some
   future").  For example, "A(work U go_home)" means "I will work
   until I go home" and "E(work U go_home)" means "I may work
   until I go home".

   (1997-01-21)