Properties of Boolean functions

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Family is a hard property. The image shows a family with eight members.

File:Zhegalkin twins in tesseract.svg

Twin is a soft property. E.g. the twin of the tautology is always the Template:W of all arguments.

Properties of Boolean functions are maps that assign values to Boolean functions.

Soft properties are dependent on arity.
For them the domain is always just the set of $2^{2^n}$ Boolean functions with arity $n$.

Hard properties are rarer, and probably more useful.
For them the domain can be the infinite set of all Boolean functions. (Typically the codomain will also be infinite, unless the values are Boolean.)

Properties of 3-ary BF are illustrated here: Boolf prop/3-ary
E.g. Boolf prop/3-ary/quaestor, Boolf prop/3-ary/patron

Below is a list of links to the respective chapters.   They are created with Template:Tl.

hard

• Template:Boolf-prop
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• Template:Boolf-prop, Template:Boolf-prop, Template:Boolf-prop
• Template:Boolf-prop, Template:Boolf-prop, Template:Boolf-prop
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• Template:Boolf-prop, Template:Boolf-prop
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binary

• Template:Boolf-prop
• Template:Boolf-prop, Template:Boolf-prop
• Template:Boolf-prop, Template:Boolf-prop, Template:Boolf-prop
• Template:Boolf-prop, Template:Boolf-prop
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• Template:Boolf-prop, Template:Boolf-prop, Template:Boolf-prop
• Template:Boolf-prop, Template:Boolf-prop, Template:Boolf-prop
• Template:Boolf-prop
• Template:Boolf-prop
• Template:Boolf-prop, Template:Boolf-prop, Template:Boolf-prop
• Template:Boolf-prop, Template:Boolf-prop, Template:Boolf-prop

integer

• Template:Boolf-prop
• Template:Boolf-prop
• Template:Boolf-prop
• Template:Boolf-prop
• Template:Boolf-prop, Template:Boolf-prop

soft

• Template:Boolf-prop
• Template:Boolf-prop
• Template:Boolf-prop, Template:Boolf-prop
• Template:Boolf-prop
• Template:Boolf-prop, Template:Boolf-prop

binary

• Template:Boolf-prop, Template:Boolf-prop
• Template:Boolf-prop
• Template:Boolf-prop
• Template:Boolf-prop, Template:Boolf-prop
• Template:Boolf-prop
• Template:Boolf-prop

integer

• Template:Boolf-prop
• Template:Boolf-prop
• Template:Boolf-prop, Template:Boolf-prop
• Template:Boolf-prop, Template:Boolf-prop, Template:Boolf-prop
• Template:Boolf-prop
• Template:Boolf-prop
• Template:Boolf-prop