Definition:Modal Logic

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Modal logic is a branch of logic in which truth values are more complex than being merely true or false, and which distinguishes between different "modes" of truth.

There are two operators in classical modal logic, defined for some proposition $P$ dependent on some world $w$:

$(1): \quad$ Necessity, represented by $\Box$, defined by:
$\Box P : \iff \forall w: \map P w$
$(2): \quad$ Possibility, represented by $\Diamond$, defined by:
$\Diamond P: \iff \exists w: \map P w$

Modal logic may also have other operators, including:

Temporal logic, which uses several operators including present and future;
Epistemic logic, which uses operators "an individual knows that" and "for all an individual knows it might be true that";
Multi-Modal logic, which uses more than two unary modal operators.

Also see

  • Results about modal logic can be found here.