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词汇 iff
释义

Definition of iff in English:

iff

conjunction ɪfif
Mathematics Logic
  • If and only if.

    〔逻,数〕在…而且只有在…的条件下

    Example sentencesExamples
    • Minimalism allows us to generate a minimal truth condition for any meaningful indicative sentence, such as ‘Lying is wrong’ is true iff lying is wrong.
    • The truth conditions for negation are: A is true iff A is not true.
    • Let the letter ‘M’ represent this operator, and add to the axioms of classical propositional logic the modal axiom M (p v q) iff Mp v Mq.
    • Let us say that I could have rendered a proposition false in the weak sense iff I was able to do something such that, if I did it, the proposition would have been falsified (though not necessarily by my act, or by any event caused by my act).
    • Thus the sentence ‘Snow is white’ is true iff it corresponds to the fact that snow is white.

Origin

1950s: arbitrary extension of if.

Definition of iff in US English:

iff

conjunctionif
Logic Mathematics
  • If and only if.

    〔逻,数〕在…而且只有在…的条件下

    Example sentencesExamples
    • Thus the sentence ‘Snow is white’ is true iff it corresponds to the fact that snow is white.
    • Minimalism allows us to generate a minimal truth condition for any meaningful indicative sentence, such as ‘Lying is wrong’ is true iff lying is wrong.
    • Let the letter ‘M’ represent this operator, and add to the axioms of classical propositional logic the modal axiom M (p v q) iff Mp v Mq.
    • Let us say that I could have rendered a proposition false in the weak sense iff I was able to do something such that, if I did it, the proposition would have been falsified (though not necessarily by my act, or by any event caused by my act).
    • The truth conditions for negation are: A is true iff A is not true.

Origin

1950s: arbitrary extension of if.

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