Multiple-conclusion logic

A multiple-conclusion logic is one in which logical consequence is a relation, $\vdash$, between two sets of sentences (or propositions). $\Gamma \vdash \Delta$ is typically interpreted as meaning that whenever each element of $\Gamma$ is true, some element of $\Delta$ is true; and whenever each element of $\Delta$ is false, some element of $\Gamma$ is false.

Some logicians favor a multiple-conclusion consequence relation over the more traditional single-conclusion relation on the grounds that the latter is asymmetric (in the aesthetic, not mathematical, sense) and does favors truth over falsity (or assertion over denial).