Artificial intelligence (AI) and its potential to run amok has fascinated sci-fi enthusiasts since Isaac Asimov introduced The Three Laws Of Robotics. Ever since then, there have been various scenarios where an AI would start harming people because it saw them as a threat to whatever mission the AI and the people were carrying out (see 2001: Space Odyssey) or out of self-preservation (see The X-Files “Ghost in the Machine”). This trope culminated in The Matrix trilogy, which presented a world where machines had become the dominant species on earth and humans were reduced to a source of heat.
Person of Interest introduces a new narrative which is a sort of combination of all of the above. It starts off with an AI machine with omnipresent/omniscient abilities which was designed to detect acts of terror before they actually happen. But it detects all acts of violence, which then have to be separated into relevant (terrorism) and irrelevant (ordinary crime). While a mysterious government agency deals with the terror threats, Harold Finch (the creator of the Machine), along with John Reese, Joss Carter, Sameen Shaw, Lionel Fusco, and Root, take it upon themselves to try and prevent the ordinary crimes.