Noncommutative logic

Ordered logic, also known as non-commutative logic, is a substructural logic that denies the structural rule of exchange. The order of assumption is therefore critical; if $A$ is assumed before $B$, then $A$ must be used before $B$.

Note: ordered logic is a restriction of linear logic; as such the oft-encountered phrase non-commutative linear logic or ordered linear logic is redundant.

See also

• Linear logic