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An open square before a proposition, meaning 'necessarily'.
Also known as: Box operator, Necessarily, Modal box, Always operator
In modal logic a square before a proposition says it holds in every accessible situation. What 'accessible' means is fixed by the system, so the same square reads as 'necessarily', 'always', 'it is provable that' or 'after every execution' according to the logic in use.
Says the proposition holds at every world accessible from the current one, read as 'necessarily' in the standard modal reading.
Contexts: Mathematics
Takes a different reading in each modal system — always, provably, obligatorily, after every step — because the accessibility relation is what the system fixes.
Contexts: Mathematics
A hollow square with four equal sides, set before the proposition it governs.