A multiple-conclusion logic is one in which logical consequence is a relation

Relation (mathematics)

In set theory and logic, a relation is a property that assigns truth values to k-tuples of individuals. Typically, the property describes a possible connection between the components of a k-tuple...

, , between two sets of sentences

Sentence (mathematical logic)

In mathematical logic, a sentence of a predicate logic is a boolean-valued well formed formula with no free variables. A sentence can be viewed as expressing a proposition, something that may be true or false...

 (or propositions). is typically interpreted as meaning that whenever each element of is true, some element of is true; and whenever each element of is false, some element of is false.

This form of logic was developed in the 1970s by D. J. Shoesmith and Timothy Smiley

Timothy Smiley

Timothy John Smiley FBA is Emeritus Knightbridge Professor of Philosophy at Clare College, Cambridge University.He has edited and contributed to numerous papers and publications including:...

 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

Asymmetry

Asymmetry is the absence of, or a violation of, symmetry.-In organisms:Due to how cells divide in organisms, asymmetry in organisms is fairly usual in at least one dimension, with biological symmetry also being common in at least one dimension....

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