Multiple conclusion logic

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