Last Updated
：2025/11/24
Peirce's law
Proper noun
Japanese Meaning
命題論理における定理のひとつで、古典論理では妥当であるが直感主義論理では成り立たない。具体的には、含意のみを使う命題論理体系において排中律の代替として用いられる法則、すなわち ((P→Q)→P)→P を示す。
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(logic) The classically valid but intuitionistically non-valid formula ((P→Q)→P)→P of propositional calculus, which can be used as a substitute for the law of excluded middle in implicational propositional calculus.
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Peirce's law
When developing an implicational proof system, we found that adding Peirce's law simplifies many derivations that otherwise would require the law of excluded middle.
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When developing an implicational proof system, we found that adding Peirce's law simplifies many derivations that otherwise would require the law of excluded middle.
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