Temporal Operators
Temporal logic has two kinds of operators: logical operators and modal operators . Logical operators are usual truth-functional operators . The modal operators used in Linear Temporal Logic and Computation Tree Logic are defined as follows.
Textual | Symbolic | Definition | Explanation | Diagram |
---|---|---|---|---|
Binary operators | ||||
U | Until: holds at the current or a future position, and has to hold until that position. At that position does not have to hold any more. | |||
R | Release: releases if is true until the first position in which is true (or forever if such a position does not exist). | |||
Unary operators | ||||
N | Next: has to hold at the next state. (X is used synonymously.) | |||
F | Future: eventually has to hold (somewhere on the subsequent path). | |||
G | Globally: has to hold on the entire subsequent path. | |||
A | All: has to hold on all paths starting from the current state. | |||
E | Exists: there exists at least one path starting from the current state where holds. |
Alternate symbols:
- operator R is sometimes denoted by V
- The operator W is the weak until operator: is equivalent to
Unary operators are well-formed formulas whenever B is well-formed. Binary operators are well-formed formulas whenever B and C are well-formed.
In some logics, some operators cannot be expressed. For example, N operator cannot be expressed in Temporal Logic of Actions.
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Famous quotes containing the word temporal:
“Science is the language of the temporal world; love is that of the spiritual world. Man, indeed, describes more than he explains; while the angelic spirit sees and understands. Science saddens man; love enraptures the angel; science is still seeking, love has found. Man judges of nature in relation to itself; the angelic spirit judges of it in relation to heaven. In short to the spirits everything speaks.”
—HonorĂ© De Balzac (17991850)