What is the ruling on someone who swore not to give anything to a person, then that person took it without his knowledge, then the swearer recovered it after he found out, and is he required to offer expiation for breaking an oath?

The intention of the swearer determines what he means by his oath. So, if someone swears not to give a certain thing to a person, and that person takes it without the swearer's knowledge, the swearer does not break his oath if his intention did not include preventing the taking without his knowledge, because the basis is not giving it. Ibn Qudamah said in Al-Mughni that an oath is based on the intention of the swearer and is directed towards it, whether it agrees with the apparent meaning of the wording or contradicts it.