Definition:Modal Operator/Necessity

Definition

The necessity operator $\nec$ is the unary modal operator defined for some proposition $P$ dependent on some world $w$:

$\nec P : \iff \forall w: \map P w$

Also denoted as

The necessity operator can also be seen in the form $\map {\mathrm L} P$:

$\map {\mathrm L} P : \iff \forall w: \map P w$

for some proposition $P$ dependent on some world $w$.

Also see

• Definition:Possibility Operator

• Results about the necessity operator can be found here.

Technical Note

The $\LaTeX$ code for \(\nec\) is \nec .

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): modal logic
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): modal logic