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单词 Brouwersche axiom
释义
Brouwersche axiom

Logic
  • In modal logics with a conditional connective and unary negation and necessity operators ¬ and , the axiom scheme:

    • φ¬¬φ

    or, when a possibility operator is included:

    • φφ.

    The axiom asserts that the truth of a proposition entails that it is necessarily possible. Named after the founder of intuitionism L. E. J. Brouwer (1881–1966) due to the resemblance between the equivalent formula and the axiom governing the introduction of intuitionistic negation:

    • φ¬¬φ.

    Despite the superficial resemblance there is no clear relationship between the logic B (the smallest normal modal logic including the Brouwersche axiom) and intuitionistic logic, for which reason the resemblance is generally regarded as primarily cosmetic.


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