 A non-adjunctive system is a system that does not validate adjunction (i.e., \(\{A, B\} \not\vDash A \wedge B)\). As we saw above, discussive logic without a discussive conjunction is non-adjunctive. Another non-adjunctive strategy was suggested by Rescher and Manor (1970). In effect, we can conjoin premises, but only up to maximal consistency. Specifically, if \(\Sigma\) is a set of premises, a maximally consistent subset is any consistent subset \(\Sigma '\) such that if \(A \in \Sigma - \Sigma '\) then \(\Sigma ' \cup \{A\}\) is inconsistent. Then we say that \(A\) is a consequence of \(\Sigma\) iff \(A\) is a classical consequence of \(\Sigma '\) for some maximally consistent subset \(\Sigma '\). Then \(\{p, q\} \vDash p \wedge q\) but \(\{p, \neg p\} \not\vDash p \wedge \neg p\).