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Temporal logic was first studied in depth by Aristotle , whose writings are filled with a crude form of first order temporal modal binary logic. Any logic which uses the Existential Quantifier or the Universal Quantifier is said to be a First Order Logic . Any logic which views time as a sequence of States is a temporal logic, and any logic which uses only two truth values is a Binary Logic .

Consider the statement: "I am hungry." Though its meaning is constant in time, the truth value of the statement can vary in time. Sometimes the statement is true, and sometimes the statement is false, but the statement is never true and false simultaneously. In a temporal logic, statements can have a truth value which can vary in time. Contrast this with an atemporal logic, which can only handle statements whose truth value is constant in time.


TEMPORAL OPERATORS

Temporal logic has two kinds of operators (
eg,\or,\and, ightarrow) and modal operators used in temporal logic are defined as follows:

Note: \phi denotes a path and \psi denotes a state.

Alternate symbols:
  • operator N is sometimes noted '''X'''

  • operator R is sometimes noted '''V''' or '''W'''


Unary opearators are Well-formed Formula s whenever B(\phi) is well-formed. Binary operators are well-formed formulas whenever B(\phi) and C(\phi) are well-formed.

In some logics, some operators cannot be expressed. For example, N operator cannot be expressed in Temporal Logic Of Actions .


TEMPORAL LOGICS


Temporal logics include


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