Multiple-conclusion logic explained

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.

This form of logic was developed in the 1970s by D. J. Shoesmith and Timothy Smiley^[1] 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

References

1. D. J. Shoesmith and T. J. Smiley, Multiple Conclusion Logic, Cambridge University Press, 1978