In L.C. 922, mankind faces a sudden crisis.

In Tetra Heaven, the land of legend, a hundred years of war have come to an end. The evil gods who lost the war search for a new place to live, and found it in Septpia, the human world, which they proceed to invade.

The Logicalists attached to ALCA (the Another Logic Counter Agency), a special police agency whose duty it is to protect cities from assaults by foreigners, are compelled to act in defence of cities, whether they wish to do so or not. Utilizing their special ability, Logicalists can initiate Trance with goddesses from the other world, to stand a fighting chance on the battlefield.

Tsurugi Yoshichika lost his Logic card in a battle in Hong Kong a few years back, now living happily with his father Rentarou and younger sister Shiori as a civilian. But one day he is caught up in an attack on a shopping mall, where he meets a beautiful goddess named Athena. In her hands she holds Yoshichika's Logic card, letting them both fight the evil beings from Tetra Heaven.

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Other: Watashitachi, Luck Logic Bu!
Same setting: Hina Logi: From Luck & Logic