More General

Let $\sigma$ and $\theta$ be substitutions and $W\subseteq {\mathcal{V}}_l$ a subset of variables. We say that $\sigma$ is more general than $\theta$ : $\sigma \le \theta [W]$ iff there is a substitution $\rho$ such that $\theta =(\rho \circ \sigma )[W]$ where $\sigma =\rho [W]$ iff $\sigma (X)=\rho (X)\forall X\in W$.

In other words a substitution $\sigma$ is more general than the substitution $\theta$ when we can get to $\theta$ by further substitution in $\sigma$.

We do the restriction on $W$ because thats what is needed to prove all of this xD.

Also see:

• Most General Unifier