Luck & Logic
In the year L.C. 922, people faced a sudden crisis. In Tetra Heaven, the land of legend, a hundred years of war had come to a close. The gods who lost the war searched for a new place to live, and found it in Septpia, the human world, which they proceeded to attack. The Logicalists attached to ALCA, a special police agency whose duty it was to protect cities from assaults by foreigners (angels), were compelled to act in defense of cities, whether they wished to or not. Depending on their ability, Logicalists could initiate trance with goddesses from the other world, and stand a fighting chance on the battlefield. A civilian named Yoshichika Tsurugi, who lacked "Logic" and lived happily with his family, was caught up in an attack, and took shelter along with many people. He meets a beautiful goddess named Athena. In her hands, she had the "Logic" that Yoshichika lacked. Now both Yoshichika and Athena head to their destiny.
Episodes12
Hero or Mob
A high-school-age boy named Yoshichika Tsurugi, who was formerly an ALCA Logicalist until he lost his Logic, finds himself caught between protecting his family as a civilian from otherworldly incursions and rejoining ALCA when his Logic is found.
Genius or Fool
Yoshichika is obliged to go through a two-day trial period to be reinstated to ALCA, during which he excels at his tests and manages to step on his team leader's toes. Yoshichika meets Olga, and is curious about the special treatment he receives.
Dream or Reality
After Tamaki is replaced as team leader by Yoshichika, she is devastated. Yoshichika learns from Veronica about how he and Tamaki are not that much different in their respect for life. Veronica must take combat matters into her own hands.
Freedom or Restraint
Chloe becomes occupied with investigating the Paradox Level 9.8 readings that previously appeared, stepping on the toes of the designated research staff. Chloe disobeys orders to tackle a Foreigner on her own.
Yesterday or Tomorrow
Yoshichika and Yukari discover that Mana was abandoned as a child, and that even now, she hopes to contact her parents again. When a Foreigner shows up that proves too difficult for Chloe and Tamaki to handle, Mana makes a stunning decision.
Battle or Surrender
Yukari dreams of doing more as a Logicalist, but her lack of experience and inability to Trance with any of the others during training sessions holds her back. A crisis in the Foreigner holding facility threatens the entire branch.
Human or God
The ALCA members get some rare time off, and Shiori invites them over to the Tsurugi home under the false pretense that it is Yoshichika's birthday. A misunderstanding drives a wedge between Yoshichika and Athena.
Guilt or Innocence
When Veronica's Paradox Sick former trainer, Ash Paxton, is suddenly moved to Sapporo, she tenders her resignation to pursue him. Director Jarno, wary about events taking place at the ALCA lab in Sapporo, charges Yoshichika to protect Veronica.
Enemy or Friend
As the ALCA members improve their skills, Olga feels more and more like he is being left behind without a Foreigner to Covenant with. Lucifer pays a surprise visit to the ALCA Naien office with an unexpected proposal.
Heaven or Hell
After Olga goes missing with his Logigraph, Yukari and Quetzie fly out and find him with Lucifer. Lucifer reveals to Olga what his plans are concerning Septpia, humanity, and the displaced archdemons of Tetra-Heaven.
Despair or Destruction
It's all hands on deck for the Naien branch of ALCA when they are cut off from headquarters and all of their Foreigners are on the loose. With all other options exhausted, Yoshichika and Athena make a fateful decision in order to stop Olga.
Luck and Logic
Yoshichika and Athena confront Olga and Lucifer for a final showdown atop ALCA Headquarters. The Logicalists and goddesses deal with the fallout left in the wake of the end of the conflict.