What is the ruling regarding a divorce oath (yamin talaq) uttered by a man to his wife, contingent on his sister returning to her ex-husband, given that his sister did return and was then divorced again? Is he now obligated to offer expiation for the oath after he swore that if he were to inquire about his sister, his wife would be divorced?

Revoking an oath of divorce, such as an oath that your sister will not return to her husband, results in divorce. If you intended to repeat the oath as a new تأسيس (establishment), then divorces occur according to the number of repetitions. If you intended it as an تأكيد (affirmation), then it is one divorce. Ibn Taymiyyah held the view that it is an oath that requires expiation. If you made your wife's divorce contingent on your speaking to your sister if she returns to her husband, then whenever you speak to her, divorce occurs. If you do not speak to her, you incur sin for cutting off kinship ties. If you intended that if you speak to your sister when she returns to her husband, your wife is divorced, then only one divorce occurs. It is advisable to refer to the Sharia (definition) courts.