should

cho7712that he should have

It simply means "that this happened."
I'm surprised that he should have thought I'd help him.

It has nothing to do with obligation or attitude.

Thank you for the answer.
According to you, 'should' does not bear any significant meaning. Is there a particular reason to use should in such cases?

They're both imagined situations.

It works like an idiom. You just have to "know what it means" in this particular framework.
It's a a bit uncommon these days, but educated native speakers would be familiar with it.
The more common meanings of "should" are well known.
(Eg., You should eat more vegetables.)

Hiya11 They're both imagined situations.

I disagree.

In "I'm surprised that he should have lost the match," we're talking about something that has actually happened.
This particular usage is somewhat "literary," and is unfamiliar to most people.

cho7712Thank you for the answer.According to you, 'should' does not bear any significant meaning. Is there a particular reason to use should in such cases?

It's not just about "should". "should have" is there as a unit that is not necessary to the meaning of the sentences. The more common way to write the sentences is without "should have".

cho7712Is there a particular reason to use should in such cases?

This is of course the $64,000 question.
I agree with Canadian that it's not "necessary," but great literature is full of stuff which is not necessary.
This usage is highly stylized and probably borders on obsolescence.
I'm not prepared to offer a convincing argument for its use "in su