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temporal logic
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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".