Multiple-conclusion logic

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

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