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In logic and mathematics, the minimal negation operator is a multigrade operator where each is a kary boolean function defined in such a way that if and only if exactly one of the arguments is 0.
In contexts where the initial letter is understood, the mno's can be indicated by argument lists in parentheses. The first four members of this family of operators are shown below, with paraphrases in a couple of other notations, where tildes and primes, respectively, indicate logical negation.
It may also be noted that is the same function as and , and that the inclusive disjunctions indicated for and for may be replaced with exclusive disjunctions without affecting the meaning, because the terms disjoined are already disjoint. However, the function is not the same thing as the function .
The minimal negation operator (mno) has a legion of aliases: logical boundary operator, limen operator, threshold operator, or least action operator, to name but a few. The rationale for these names is visible in the Venn diagrams of the corresponding operations on sets.
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