Definition:Modal Operator

Definition

The modal operators are the operators in modal logic defined as follows:

Necessity

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

$\nec P : \iff \forall w: \map P w$

Possibility

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 see

• Results about modal operators can be found here.

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