Luck and Logic

Japanese Title: ラクエンロジック

Plot
In the year L.C. 922, mankind faces an unprecedented crisis. Following the conclusion of a hundred-year war on the mythical world of Tetraheaven, the losing Majins sought a safe haven and invaded the human world Septpia. The government is forced to fight by employing Logicalists belonging to ALCA, a special police that protects the streets from foreigners of another world. Logicalists are given a special power that allows them to enter a trance with Goddesses from the other world.

One day, Yoshichika Tsurugi, a civilian who is lacking "Logic" and lives peacefully with his family, meets the beautiful goddess Athena while helping people escape from a Majin attack. She wields the "Logic" that Yoshichika should have lost. This leads Yoshichika to an unexpected destiny with Athena.