The film will allegedly take its cues from the original 1967 novel written by William F. Nolan and George Clayton Johnson, not the 1976 sci-fi flick starring Michael York and Farrah Fawcett. The story of Logan's Run takes place in a future society where everyone is commanded to die upon reaching a certain age. Those who resist the order are deemed "runners" and become targets of a group of operatives called "Sandmen." The titular Logan is a Sandman who winds up on the run.
Garland is well known for his collaborations with director Danny Boyle, having written the screenplays for 28 Days Later and Sunshine. He also wrote The Beach, the novel that Boyle adapted into the Leonardo DiCaprio-starring film in 2000. In the comic book world, Garland has reportedly written the script for a forthcoming Judge Dredd reboot.
Source: Heat Vision