# Definition:Modal Logic

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## Definition

**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.

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## Also see

- Results about
**modal logic**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**