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  "body": "\n## Summary\n\nA **multiple-conclusion logic** is one in which logical consequence is a relation, $\\vdash$, between two [[sets|0BSJ7RQ9BW]] 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. Such a reading is related to Gerhard Gentzen's interpretation of the multiple-succedent sequent calculus LK, though Gentzen interprets his sequents $\\Gamma\\vdash\\Delta$ as formulae $(\\bigwedge\\Gamma)\\supset(\\bigvee\\Delta)$.\n",
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