1

In this case, the sentence reads "You must have made your weekly claim for benefits for the week ending [date] by [date]".

This is referring to the fact that a person claimed a week of benefits too late, and should have claimed them earlier. However, while "must" is generally considered a stronger word, in this case it sounds more like we are saying "We think you claimed benefits this date, but we're not sure." Am I correct in reading it this way? Would the sentence be clearer if it said "You SHOULD have made your weekly claim for benefits for the week ending [date] by [date]"?

2

I agree with you. Most modals have a deontic sense (about necessities and obligations, and effects in the world) and an epistemic sense (about people's knowledge about the world).

"Must" is usually deontic when followed by a simple verb,

You must go tomorrow.

but when followed by the so-called "perfect infinitive" - "have" + past-participle - it is much more likely to be epistemic.

You must have been there!

This is much less so for "should": "should have" may be deontic:

You should have left immediately.

or epistemic:

They should have got home by now. I'll try ringing them.

0

This sentence:

You must have made your weekly claim …

is a logical conclusion of what actually happened. We observe some facts, and conclude that you did make you weekly claim as described - otherwise the observed facts would have been different.

If you change it to:

You should have made your weekly claim …

the meaning changes completely. Now it is a statement about what should have happened, but didn't. You did not make your weekly claim as described, although you should have.

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