Not sure if it's the correct word, but I think "continue" is the better word to use here.

Mining has no memory, it's not like you are downloading or uploading something which will cause you an issue if your power goes out, you are randomly guessing a random number and every share you submit is completely independent of all the other shares you did/will submit.

Another way to look it at, assume your miner can hash at speed of 24 hashes per 24 hours, so if your miner is online for the whole day, it will have 24 chances of finding a block, if the power goes out for 4 hours, your miner will have 20 chances of finding a block, so while that reduces your overall chances of finding a block due to fewer shares being submitted, it has NO impact on your previous hashes (which are now useless anyway) nor your future hashes.