Mathematical Left White Square Bracket

It opens a specialized pair; the notation decides what it marks. The double bracket meaning depends on its field: in formal semantics, ⟦M⟧ names M’s denotation—the mathematical object or truth value assigned to a linguistic expression or program.

In the 1960s, Dana Scott moved from double bars to square brackets for a formula’s truth value as formulas grew longer. His 1967 work is an early printed example of brackets used for denotation. This history is why the semantic notation bears Scott’s name.

Why does the same pair also mark a bag?

In Z notation, it encloses a multiset.

⟦B⟧ can denote a bag: a collection where duplicate items are kept and their count matters. This is a separate notation convention, so identify it from the surrounding Z specification rather than from the brackets alone.