Any deductive system $\text{L}$ with a conjunction $\wedge$ for which the inference of adjunction is not valid. Alternatively, a logic $\text{L}$ is non-adjunctive if there exists some $\text{L}$-theory $T$ including two formulae $\phi$ and $\psi$ such that $\phi \wedge \psi \notin T$. The most well-known example of a non-adjunctive logic is discursive logic.