[throw219080123]

True. But if the system is implemented by a country this could be implemented using the law system and insurances.

For example, when each transaction is done, both parties might keep a cryptographic proof which they are required to submit once they are online again.

Failing to submit could result in a small fine (to encourage submission) and double spending which can then be detected could result in a large fine (or even a prison sentence), for example.

There is, perhaps, a privacy issue, just like with blockchain. But it's not more of an issue than online transactions.

[mosdl]

You don't need a blockchain for that, see how old credit cards worked without network access.

[throw219080123]

I didn't say you need a blockchain. I just said a cryptographic protocol (mostly offline and unrelated to blockchain) would help to automatically and quickly detect and proof fraud.

The offline credit card system does not proof fraud but just has insurance.