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In logic, a rule of inference is admissible in a formal system if the set of theorems of the system does not change when that rule is added to the existing rules of the system. In other words, every formula that can be derived using that rule is already derivable without that rule, so, in a sense, it is redundant. The concept of an admissible rule was introduced by Paul Lorenzen (1955).

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  • Zulässige Regel (de)
  • Admissible rule (en)
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  • In logic, a rule of inference is admissible in a formal system if the set of theorems of the system does not change when that rule is added to the existing rules of the system. In other words, every formula that can be derived using that rule is already derivable without that rule, so, in a sense, it is redundant. The concept of an admissible rule was introduced by Paul Lorenzen (1955). (en)
  • Eine Schlussregel heißt zulässig in Bezug auf einen Kalkül, wenn jede Formel des Kalküls, die in dem Kalkül mit Verwendung dieser Regel hergeleitet werden kann, bereits auch ohne Verwendung dieser Regel hergeleitet werden kann. Auf diese Weise lassen sich Gültigkeitsbeweise von Regeln durchführen: Ist eine Regel wie etwa die Schnittregel in einem Kalkül zulässig, also eliminierbar, so ist sie in dem Kalkül gültig. (de)
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