 There are several ways of generalizing the semantics and making room for additional sentential negations. One comes with giving up bivalence and admitting sets of truth values (truth degrees) with more than two elements, see the entry on  many-valued logic.  In the so-called Łukasiewicz many-valued logics Ł\(_{\aleph_{1}}\), Ł\(_{\aleph_{o}}\), and Ł\(_n\), the set of values is either the whole real unit interval [0,1], or the whole rational unit interval [0,1], or the finite set of rational numbers \(\{ 0, \frac{1}{n-1}, \frac{2}{n-1}, \ldots, 1 \}\). These sets include 1 as the designated value representing True, where the designated values of a many-valued logic are the values that are preserved in valid inferences. Łukasiewicz negation \(\osim \) is defined by setting \(f_{\osim }(u) = 1- u\). Negation is thus understood in terms of subtraction from the numerical representation of True. In so-called Gödel many-valued logics, the truth function \(f_{\osim }\) for negation \(\osim \) is defined by setting \(f_{\osim }(u) = 1\) if \(u = 0\), and \(f_{\osim }(u) = 0\) if \(u \not = 0\). Here negation is understood in terms of the numerical representation of True and distinctness from the numerical representation of False.