Ordering of Hypotheses

In any concept learning problem the hypothesis can be ordered in a general-to-specific ordering.
By using this ordering we can exhaustively search even infinite spaces without having to enumerate every hypothesis.
For example, \[h_1 = \langle Sunny, ?, ?, Strong, ?, ?\rangle\] is more specific than \[h_2 = \langle Sunny, ?, ?, ?, ?, ?\rangle\]
Or, $h_2$ is more general than $h_1$.
Any example that is classified as positive by $h_1$ will also be classified as positive by $h_2$.
If $h_j$ and $h_k$ are boolean-valued functions defined over X then $h_j$ is more general than or equal to $h_k$ (written $h_j \geq_g h_k$) if and only if \[ \forall_{x \in X}[(h_k(x)=1) \rightarrow (h_j(x)=1)]\]