Minimal negation operator
From Psychology Wiki
Community portal · Tasks to do · News · Help
Clinical · Educational · Ind&Org · Other fields · Professional · Transpersonal · World
Assessment |
Biopsychology |
Comparative |
Cognitive |
Developmental |
Language
Personality |
Philosophy |
Research Methods |
Social |
Statistics
Statistics: Scientific method · Research methods · Experimental design · Undergraduate statistics courses · Statistical tests · Game theory · Decision theory
In logic and mathematics, the minimal negation operator 
is a multigrade operator 
where each 
is a k-ary 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.
[edit] See also
| This page uses content from the English-language version of Wikipedia. The original article was at Minimal negation operator. The list of authors can be seen in the page history. As with Psychology Wiki, the text of Wikipedia is available under the GNU Free Documentation License. |
