Is "should" or "shouldn't" appropriate in this sentence?

Question

The concept is that whatever is being asked, is negated when expressing uncertainty or confirmation from the recipient.

You do know what's up, don't you?
They won't show up, will they?

But what if the negation is semantic not grammatical?

1. That should hardly matter, shouldn't it?
2. That should hardly matter, should it?

Answer 1

'Hardly' makes the main clause negative, so the question tag should be in affirmative form. Whatever auxiliary verb appears in the main clause should usually be repeated in the question tag. This applies to most (all?) semantically negative adverbs placed before the main verb. If there is no auxiliary verb, use do in the correct tense. The exceptions are 'to be' (repeat 'be' in the right tense and to have (you can choose between 'do' and 'have').

• That should hardly matter, should it?
• John has very little money, doesn't/hasn't he?
• Claudia can do almost nothing to help, can she?
• Idle talk seldom helps, does it?
• Ali rarely visits his aunt, does he?

But adjectives that have a negative meaning usually take a negative question tag. The same applies to adverbs placed (correctly) after the verb:

• Fido would make a poor bloodhound, wouldn't he?
• Fido performed poorly at the dog show, didn't he?
• Ali visits his aunt very rarely, doesn't he?

Be careful what you consider a negative meaning. 'slowly', for example, is not usually semantically negative, nor is to 'stay/go/become quiet'.

• She opened the door slowly, didn't she?
• Roxette always barks when I come in, but stays quiet when you do, doesn't she?

You can of course also say (for example):

• Fido performed poorly at the dog show, did he?

but that changes the meaning a little. The sentence is no longer an affirmative sentence inviting (and possibly expecting) a confirmation from the listener but rather a real question. The speaker really wants to know whether poor old Fido scored poorly in the competition.