Computational Tree Logic

It uses s and Temporal Operator s.

vs CTL -->

OPERATORS

Logical operators

The logical operators are the usual ones:

eg,\or,\and,
ightarrow

and

\leftrightarrow

. Along with these operators CTL formulas can also make use of the boolean constants True and False .

Temporal operators

The temporal operators are the following:

N $\phi$ - Next: $\phi$ has to hold at the next state (this operator is sometimes noted '''X''' instead of N).

G $\phi$ - Globally: $\phi$ has to hold on the entire subsequent path.

F $\phi$ - Finally: $\phi$ eventually has to hold (somewhere on the subsequent path).

A $\phi$ - All: $\phi$ has to hold on all paths starting from the current state.

E $\phi$ - Exists: there exists at least one path starting from the current state where $\phi$ holds.

$\phi$ U $\psi$ - Until: $\phi$ has to hold until at some position $\psi$ holds. This implies that $\psi$ will be verified in the future.

$\phi$ W $\psi$ - Weak until: $\phi$ has to hold until $\psi$ holds. The difference with '''U''' is that there is no guarantee that $\psi$ will ever be verified. The W operator is sometimes called "unless".

State and Path formulas

CTL formulas can be divisioned into state formulas and '''path formulas'''. Path formulas's true value depend on a path of evaluation (for example, "on this path, always p"). All other formulas are state formulas (for example, "from this state, on all paths, p").

EXAMPLES

Let P mean "I like chocolate" and Q mean "It's warm outside".

AG.P
:I will like chocolate now on, no matter what happens.

EF.P
:It's possible I may like chocolate some day, at least for one day.

AF.'''EG'''.P
:It's always possible (AF) that I will suddenly start liking chocolate for the rest of time. (Note: not just the rest of my life, since my life is finite, while G is infinite).

EG.'''AF'''.P
:This is a critical time in my life. Depending on what happens next (E), it's possible that for the rest of time (G), there will always be some time in the future (AF) when I will like chocolate. However, if the ''wrong'' thing happens next, then all bets are off and there's no guarantee about whether I'll ever like chocolate.

A(P'''U'''Q)
:From now until it's warm outside, I will like chocolate every single day. Once it's warm outside, all bets are off as to whether I'll like chocolate anymore. Oh, and it's guaranteed to be warm outside eventually, even if only for a single day.

E(('''EX'''.P)'''U'''('''AG'''.Q))
:It's possible that: there will eventually come a time when it will be warm forever (AG.Q) and that before that time there will always be ''some'' way to get me to like chocolate the next day (EX.P).

RELATIONS WITH OTHER LOGICS

as well as of the Modal Mu Calculus .

	APPAREL
	BABY
	BEAUTY
	BOOKS
	CAR TOYS
	CELL PHONES
	DVD'S
	ELECTRONICS
	GOURMET FOOD
	GROCERIES
	HEALTH & PERSONAL
	HOME & GARDEN
	JEWELRY
	MUSIC
	MUSIC INSTRUMENTS
	OFFICE PRODUCTS
	SOFTWARE
	SPORTING GOODS
	TOOLS & HARDWARE
	TOYS
	VIDEO GAMES
	SHOPPING HOME

	MORE SHOPPING...

	CATEGORIES ABOUT COMPUTATIONAL TREE LOGIC

	logic in computer science

	modal logic

Information About

Computational Tree Logic