Definition:Modal Operator/Possibility

Definition

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

$\pos P : \iff \exists w: \map P w$

Also denoted as

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

$\map {\mathrm M} P : \iff \exists w: \map P w$

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

Also see

• Definition:Necessity Operator

• Results about the possibility operator can be found here.

Technical Note

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

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