 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.

Three-valued logic is a type of formal logic that extends classical binary logic (which uses only two truth values: true and false) by introducing a third truth value. The most common interpretation of this third value is "unknown" or "indeterminate," but the specific interpretation can vary depending on the context. In three-valued logic, the three truth values are often represented as: 1. **True (T)**: Represents objects that are true.