It was natural that government affairs by Gofushimi were terminated and Kogon was deposed, but Godaigo did not even recognize that he was deposed in 1331, and took the stance that he was ruling during the whole time he was exiled in Oki, so therefore there was "no accession nor rule" of Kogon.
後伏見の政務が停止され、光厳が廃位されたのは当然であるが、後醍醐はそもそも元徳3年に自分が廃位された事実自体を認めず、隠岐に流されていた間も自分はずっと天皇に在位していたという立場をとり、従って光厳の即位と在位も“なかったこと”にされた。