Re: Minimal Negation Operators • 1

The brief description of minimal negation operators given in the previous post is enough to convey the rule of their construction.  For future reference, a more formal definition is given below.

Initial Definition

The minimal negation operator is a multigrade operator where each is a -ary boolean function defined by the rule that if and only if exactly one of the arguments is

In contexts where the initial letter is understood, minimal negation operators may be indicated by argument lists in parentheses.  In the discussion that follows a distinctive typeface will be used for logical expressions based on minimal negation operators, for example,

The first four members of this family of operators are shown below.  The third and fourth columns give paraphrases in two other notations, where tildes and primes, respectively, indicate logical negation.

Resources

• Logic Syllabus
• Boolean Function
• Multigrade Operator
• Minimal Negation Operator
• Survey of Animated Logical Graphs

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