Halliday & Matthiessen (2014: 692):
Here is an example of each of the four types:1.i [probability] There can’t be many candlestick-makers left.
1.ii [usuality] It’ll change right there in front of your eyes.
2.i [obligation] The roads should pay for themselves, like the railways.
2.ii [inclination] Voters won’t pay taxes any more.
As these examples show, the modal operators can occur in all four types. Their use is more restricted in usuality and in inclination than in the other two types; but as a class they cover all these senses. This brings out what it is that the four types of modality have in common: they are all varying degrees of polarity, different ways of construing the semantic space between the positive and negative poles.