1. The property that holds of certain binary connectives $\circ$ in a deductive system $\text{L}$ when they commute, that is, when $\phi \circ \psi$ and $\psi \circ \phi$ are logically equivalent in $\text{L}$.

2. The rules of inference for conjunction ($\wedge$) and disjunction ($\vee$) that capture the commutativity of the operations.

Sometimes the rule of permutation, i.e.,

is introduced as a property of commutativity as well.

3. In a multi-modal logic with two operators ${\square }_0$ and ${\square }_1$, the equivalence of formulae ${\square }_0{\square }_1\phi$ and ${\square }_1{\square }_0\phi$ and any rule of inference corresponding to this logical equivalence.