German Modal Verbs for Assumptions: er muss, er soll, er will

The ruleUsed subjectively, a modal verb no longer says what someone can or must do: it says how sure the speaker is, or whose claim it is.

Every modal has two lives. Er muss arbeiten normally means he is obliged to work. In the right context it means he must be working: a deduction about reality rather than a statement about duty. B2 is where the second reading starts appearing in texts, and it is easy to misread an entire paragraph by taking it literally.

The certainty scale

Modal	Degree	Example	Means
müssen	Near certainty	Er muss krank sein.	He must be ill: I'm sure.
dürfte	Probable	Er dürfte schon zu Hause sein.	He's probably home by now.
können	Possible	Das kann stimmen.	That may be true.
könnte	Possible, weaker	Er könnte recht haben.	He might be right.
mögen	Conceded possibility	Das mag sein.	That may well be.
kann nicht	Ruled out	Das kann nicht stimmen.	That can't be true.

dürfte is the one worth adding to your active range. It is the standard German for a careful estimate (Die Reparatur dürfte etwa 300 Euro kosten), and it has no single-word English equivalent.

sollen and wollen attribute the claim

These two do something different: they do not grade certainty, they name whose assertion it is. sollen reports what others say; wollen reports what the subject says about themselves.

Modal	Whose claim	Example	Means
sollen	Other people's	Er soll sehr reich sein.	He's said to be very rich.
wollen	The subject's own	Er will nichts gewusst haben.	He claims he knew nothing.

The wollen use is quietly sceptical. Er will Arzt sein does not mean he wants to be a doctor: it means he says he is one, and the speaker is not convinced.

Talking about the past

The assumption shifts into the past by putting the infinitive into the perfect, not the modal. The modal stays in the present.

Er muss krank gewesen sein. He must have been ill. Not Er musste krank sein, which is a plain obligation in the past.
Sie kann es nicht gewusst haben. She can't have known.
Er soll im Ausland gelebt haben. He's said to have lived abroad.
Sie will ihn nie getroffen haben. She claims she never met him.

Where it goes wrong

Er musste krank sein, deshalb kam er nicht.

Er muss krank gewesen sein, deshalb kam er nicht.

The preterite musste gives the objective reading: he was obliged to be ill, which is nonsense. A deduction about the past keeps the modal in the present and puts the infinitive into the perfect.

Common questions

What does 'Er soll reich sein' mean?

'He is said to be rich.' sollen used subjectively reports a claim made by other people, without the speaker endorsing it. It is not about obligation, and confusing the two readings can invert the meaning of a sentence.

How do I express a probability in German?

With a modal on the certainty scale: müssen for near-certainty, dürfte for probable, können or könnte for possible, and kann nicht to rule something out. dürfte in particular is the standard way to give a careful estimate.

How do I say 'he must have been ill'?

'Er muss krank gewesen sein': the modal stays in the present and the infinitive goes into the perfect. Putting the modal itself in the past (er musste) switches back to the literal obligation reading.