---
tag: 3AJTDAP93H
kind: concept
name: Multiple-conclusion logic
sources:
  - wikipedia: en:3748162@r1328744586
    locator: Multiple-conclusion logic
    note: adopted
    mention: wikipedia://en/3748162
    sections: [Summary]
same_as:
  wikidata: Q6934867
  wikipedia: Multiple-conclusion logic
inventory: [84RVJ504GH]
---

## Summary

A **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 $(\bigwedge\Gamma)\supset(\bigvee\Delta)$.