"Logic" is the concept that governs emotions, abilities, ideals, memories, and all other abstract properties that make up life in various worlds. With its power, however, alien "Foreigners" are able to pass through portals imbued with their respective world's Logic and pose a threat to other worlds. To counter this problem, the Another Logic Counter Agency (ALCA) from the human world of Septpia employs "Logicalists," people with the power to form bonds with the Foreigners who seek peace and share their Logic, tasked with dealing with all possible dangers. After overloading his powers two years prior, Yoshichika Tsurugi has lost the ability to use Logic in combat, making him no different from a regular citizen. However, his life soon returns to the battlefield when he meets Athena, a Foreigner goddess from the world of Tetra-Heaven. She brings Yoshichika his missing Logic Card, allowing him to become a Logicalist once again. Soon after, Yoshichika forms a contract with Athena and joins ALCA. There, he meets other Logicalists, and only by working with them can he hope to bring an end to the threats once and for all. [Written by MAL Rewrite]

Chihiro Enomoto is a freshman that just got to a new school called Rikkyoin High School. He lost his parents in a traffic accident when he was 10. Since then, he has been living only with his elder sister Shinobu. He is good at cooking and cleaning, and does all the housekeeping jobs. He fell in love with Tokino at first sight when he met her in the school library on the first day of school. Another girl named Ritsuko, a childhood friend of Chihiro and the chair of student council, falls in the love with the boy instantly after this long-awaited reunion. But she is not the only one who is in love with him. This is the story about a one-year campaign among the candidates for the next students government leaders, who are also chosen by the lot (kujibiki), in order to gain the position. (Source: ANN)

Dr. Taylor was on a paleontology mission with his son, Max in Africa. Rex, Max's best friend, joins along as well. When Max had stumbled across some magic stone slabs with images of dinosaurs, the boys and their friend Zoe were being called out by the dinosaurs for help. It seems that an evil organization called the "Alpha Gang," led by the nefarious Dr. Z, traveled back in time to hunt down the dinosaurs so that they could take over the world by using those dinosaurs. It is up to Max, Rex, and their friend Zoe to travel around the world, defeating Dr. Z and the Alpha Gang while hunting down the dinosaurs. (Source: Wikipedia)

Some time ago, the influential and powerful Toue Inc. bought the island of Midorijima, Japan, with the plans of building Platinum Jail—a luxurious utopian facility. Those who are lucky enough to call it home are the wealthiest citizens in the world. The original residents of the island, however, were forced to relocate to the Old Residential District; and after the completion of Platinum Jail, they were completely abandoned. "Rib" and "Rhyme" are the most common games played on the island. Rib is an old school game in which gangs engage in turf wars against each other, while Rhyme is a technologically advanced game wherein participants fight in a virtual reality. To be able to play Rhyme, you must have an "All-Mate" (an AI that typically looks like a pet), and the match must be mediated by an "Usui." Aoba Seragaki has no interest in playing either game; he prefers to live a peaceful life with his grandmother and All-Mate, Ren. However, after getting forcefully dragged into a dangerous Rhyme match and hearing rumors about disappearing Rib players, all of Aoba's hopes of living a normal life are completely abolished.