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

This form of logic was developed in the 1970s by D. J. Shoesmith and Timothy Smiley but has not been widely adopted.

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 informal, non-mathematical sense) and favors truth over falsity (or assertion over denial).