TeXipedia

Box

Represents a hollow square box symbol commonly used in mathematical logic and modal operators.

Overview

Serves as a fundamental operator in modal logic and mathematical proofs, particularly in formal reasoning and theorem statements.

  • Essential in modal logic to express necessity or obligation
  • Frequently appears in formal mathematical proofs and logical derivations
  • Often paired with diamond (◇) operator in modal systems
  • Used in computer science for expressing temporal logic properties
  • Common in philosophical logic and formal semantics

Examples

Modal logic necessity operator in a logical formula

□p→p\Box p \rightarrow p 
\Box p \rightarrow p

Expressing a modal logic axiom showing nested necessity

□p→□□p\Box p \rightarrow \Box\Box p 
\Box p \rightarrow \Box\Box p

Modal logic formula combining necessity and possibility operators

□(p∨q)↔(□p∨□q)\Box(p \lor q) \leftrightarrow (\Box p \lor \Box q) 
\Box(p \lor q) \leftrightarrow (\Box p \lor \Box q)