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Let Webb function in multi-valued logic as $Webb(x, y) = W(x, y) = Inc(Max(x, y))$. There is a theorem about any function in any multi-valued logic can be represented through the Webb function.

Then basic logic operations (negation, conjunction and disjunction) can be represented by following way for ordinary binary logic:

~x = W(x, x)     x & y = ~(~x | ~y) = W(W(x, x), W(y, y)) x | y = Inc(W(x, y)) = W(W(x, y), W(x, y)) 

And for ternary logic:

Inc(x) = W(x, x) Dec(x) = Inc(Inc(x)) ~x = W(W(Dec(x), Inc(x)), Inc(W(Dec(x), x)) x & y = ~(~x | ~y) x | y = Inc(Inc(W(x, y)) 

What is the generalized formula for basic logic operations in any multi-valued logic through the Webb function, especially negation?

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    A reference to the source of the theorem you mention would be helpful.2012-12-09

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