 Grzegorz Malinowski (1990, 1994) takes advantage of this proposal to give a counterexample to Suszko’s Thesis. He defines the notion of a single-conclusion quasi-consequence \((q\)-consequence) relation. The semantic counterpart of \(q\)-consequence is called \(q\)-entailment. Single-conclusion \(q\)-entailment is defined by requiring that if no premise is antidesignated, the conclusion is designated. Malinowski (1990) proved that for every structural \(q\)-consequence relation, there exists a characterizing class of \(q\)-matrices, matrices which in addition to a subset \(\mathcal{D}^{+}\) of designated values comprise a disjoint subset \(\mathcal{D}^-\) of antidesignated values. Not every \(q\)-consequence relation has a bivalent semantics.