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Multiple-conclusion logic : ウィキペディア英語版
Multiple-conclusion logic
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〔D. J. Shoesmith and T. J. Smiley, ''Multiple Conclusion Logic'', Cambridge University Press, 1978〕 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

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