Type (model theory)

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

See also

• Sequent calculus

References

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