Monotonicity

The underlying semantics of the auto-completion mechanism dictate that every iteration defined in Section 4.5 on a lattice L of relationship descriptions is monotone. Formally, a function f: L $\rightarrow$ L is monotonic iff $\forall$ x,y $\in$ S, x $\le$ y $\Longrightarrow$ f(x) $\le$ f(y). where S denotes a set of all possible subsets of relationships and L=(S,$\subseteq$). The monotonicity property guarantees an end to the fixed-point iterations.