Transitive Closure

The transitive closure of a binary Relation $R$ on a Set $X$ is the minimal Transitive relation $R'$ on $X$ that contains $R$. Thus $a R' b$ for any elements $a$ and $b$ of $X$ provided that there exist $c_0$, $c_1$, ..., $c_n$ with $c_0=a$, $c_n=b$, and $c_rRc_{r+1}$ for all $0\leq r<n$.

See also Reflexive Closure, Transitive Reduction