Philosophy:Multiple-conclusion logic

Short description: Mathematical logic

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

See also

• Sequent calculus