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单词 Scott’s axiom
释义
Scott’s axiom

Logic
  • An axiom scheme encountered in the study of intuitionistic and superintuitionistic logics:

    • ((¬¬φφ)(φ¬φ))(¬φ¬¬φ)

    The antecedent can be recognized as the stability principle that every formula that is stable is decidable and the consequent is the statement that φ is testable. Hence, Scott’s axiom can be read as the thesis that every formula for which the stability principle holds is testable. Scott’s axiom, named for mathematician Dana Scott (1932– ), is remarkable in that its inclusion to intuitionistic logic yields a logic (called Scott’s logic) that is not characterized by an elementary class of Kripke frames, i.e., one corresponding to a first-order property.


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