Yes, but the merchant has to have a way to check for double-spending, or otherwise verify that the signed txn they have been given represents money that can be "taken to the bank".
Checking the signature on some blob that says "this be money" is not enough.
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.
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.
I figure you can ‘solve’ it socially and legally by treating double spend while offline the same as writing a bad check. Recipients of offline transactions knowing the risk would limit it to small amounts and or emergencies.
Checking the signature on some blob that says "this be money" is not enough.