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It is interesting to me that there does not appear to be a single word conveying the logical notion of "if and only if", a.k.a. bi-implication.

Is there any example of such a word?

("Is", as a predicate in logic, can be linked to the equivalence relation '=', but this is not the same. "If and only if" is an operation on logical formulae, meaning it takes two propositions as its arguments, rather than two terms).

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    Joke on the side: the great mathematician Serre remarked that in the notation of mathematical research papers, "if and only if" became iff, "si et seulement si" became sssi, and "dann und nur dann" became dannnnn.
    – Chris Sanders
    Commented Oct 10 at 5:12
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    For those of us not conversant in formal logic, can you explain how the difference between taking two propositions rather than two terms would translate to natural language? As it is, I don’t really understand what the difference would be. ‘If and only if’ doesn’t really mean anything different from plain ‘if’ in natural language, except inasmuch as it emphasises the required nature of the condition; in that way, it’s no different from ‘when and only when’, ‘this and only this’ or any other ‘X and only X’ construction.
    – Janus Bahs Jacquet
    Commented Oct 10 at 11:16
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    @JanusBahsJacquet IFF means A implies B and B implies A. "I'm breathing if and only if I'm alive" -> "If I'm breathing, then I'm alive" and "If I'm alive, I'm breathing." Where one is true, the other must. (Hey there Julius! Wondering where you've been. Saw your proposal on Codidact. )
    – J D
    Commented Oct 11 at 8:16
  • Could be languages like Quechua. Even "if and only if" is an artificial term, some languages creates sense and squize it to one word. One such example is Quechua.
    – Juandev
    Commented Oct 16 at 14:54
  • English does have this: iff. It is very commonly used in ordinary language and casual conversation by mathematicians, computer scientists, and logicians.
    – apropos
    Commented Oct 16 at 20:41

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