The Thought Matrix was a revolutionary robotic brain created by Professor Alistair Gryffen in the mid-21st century. It allowed robots to think for themselves rather than be programmed. The K9 models of the 51st century, being descended from these sort of advances, were able to think for themselves. K9 Mark 2 didn't consider the Thought Matrix revolutionary but as Gryffen explained: (TV: Robot Gladiators)
Such sophistication may be the norm for the future, but the time I'm talking about, robots were little more than wind-up toys.