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?