= Three-valued logic
A three-valued logic uses three truth values together with specified <logical connectives> and a rule for which values count as designated truth. The truth-value set alone does not determine the logic. A third value can represent incomplete information, but its intended interpretation and inference rules must also be supplied.
For a concrete strong-Kleene semantics, take $F=0$, $U=1/2$, $T=1$ and define negation by $\neg x=1-x$, conjunction by $\min(x,y)$ and disjunction by $\max(x,y)$. Then $U\wedge F=F$ and $U\vee T=T$, while $U\vee\neg U=U$. If only $T$ is designated, the <law of excluded middle> is not valid for every valuation in this semantics.
Another three-valued semantics can use implication $x\Rightarrow y=\min(1,1-x+y)$. It makes $U\Rightarrow U=T$, whereas defining implication as $\neg x\vee y$ would give $U$. This explicit difference shows why one cannot reason from the number of values without specifying the connective tables and designated values.
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