[CG] Re: Minimal Negation Operators

Cf: Minimal Negation Operators • 2 https://inquiryintoinquiry.com/2017/08/30/minimal-negation-operators-2/ 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” ν (Greek nu) is a multigrade operator (νₖ | k∈N), where each νₖ (for k in the set of non-negative integers N) is a k-ary boolean function defined by the rule that νₖ(x₁, …, xₖ) = 1 if and only if exactly one of the arguments xₘ is 0. In contexts where the initial letter ν is understood, the minimal negation operators may be indicated by argument lists in parentheses. In what follows a distinctive typeface will be used for logical expressions based on minimal negation operators, for example, (x , y , z) = ν(x, y, z). 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. Figure 1. Minimal Negation Operators ν₀, ν₁, ν₂, ν₃ https://inquiryintoinquiry.files.wordpress.com/2021/09/minimal-negation-ope… Resources ========= Logic Syllabus https://oeis.org/wiki/Logic_Syllabus Boolean Function https://oeis.org/wiki/Boolean_function Multigrade Operator https://oeis.org/wiki/Multigrade_operator Minimal Negation Operator https://oeis.org/wiki/Minimal_negation_operator Survey of Animated Logical Graphs https://inquiryintoinquiry.com/2021/05/01/survey-of-animated-logical-graphs… Regards, Jon