Describes any deductive system $\text{L}$ with a negation $\neg$ and disjunction $\vee$ for which the principle of excluded middle fails, that is, for which the corresponding consequence relation ${⊢}_{\text{L}}$ does not satisfy the following:

• • $\text{Γ}{⊢}_{\text{L}}\phi \vee \neg \phi$ for all sets of formula $\text{Γ}\cup \left\{\phi \right\}$

Modelled theoretically, this can be formulated as the condition that every model makes true every instance of $\phi \vee \neg \phi$. The property of paracompleteness is dual to the property of paraconsistency that holds of a logic $\text{L}$ when the principle of explosion fails, that is, there exists a non-trivial model of a contradiction.