Cogitator, along with Logic Engine, are the Imperium of Man's pet term for computers. While out and out artificial intelligence is Heresy, more simple non AI computerization is allowed and for simple things such as data entry, processing bio feedback in power armor, basic targeting for Tarantulas and torpedo guidance systems are often used. What constitutes an AI is a matter open for debate, for example a Land Raider is capable of functioning on it's own killing enemies of the Imperium even if it's crew are all killed. At the same time are always a few of the more radical members of the Mechanicus willing to push said boundaries, regardless of the risks of being found out or going too far down that path. There are either probably chunks of human brain in there somewhere one way or another or the Imperium of Man just does not know what an AI is and just attributes any decision making made to the machine spirit. "AI" is just any amount of machine intelligence after all, a roomba has AI after all.
Most Cogitators are depicted as being electrical or electro-mechanical in nature, and are often shown to be as complex as a late-70's mainframe computer. They are often described as interfacing with "data-spools" and other early-industrial mechanical terms. This term may be used to delineate them from more autonomous systems, like the light-based neural-pathway-replicating vat-grown-crystal AI cores that have been shown to run advanced automated defenses for things like secure Imperial military facilities, Mechanicum temples, and noble mansions. The Adeptus Mechanicus don't purge those crystal AI things mostly because they are physically incapable of learning. Side note, those AI are designed by replicating the brain activity of lower lifeforms, like dogs, and modifying it to integrate with whatever weapons and security systems need to be controlled autonomously. The intent is to create something which will perform instinctive and unwavering guard duty, but imagine being the poor pseudo-creature to wake up immobile and instinctively compelled to guard a random building for all eternity.
Cogitators can vary greatly in complexity, mostly based on how much of a fuck the AdMech gave at that day. The most simple cogitators can be fully mechanical (as in cogs and shit) and can still be found on fucking space ships. The most complex cogitators are actually useful and often contain parts of human brains/bio-matter, like the Transmat link which are used to connect temples of the AdMech with each other and the High Altar of Technology. Some cogitators can be connected with each other, creating some sort of internet. Such networks are common on forge-worlds and some hive cities.
All cogitators contain an (usually complex) Machine Spirit and are prone for fuck ups if not well maintained. Golden rule on cogitator usage: the more important an cogitator is for the AdMech or the Inquisition the better the thing will work. The older the thing is the better the thing is. So get a old and well maintained one or prepare your anus. And watch out for computer viruses. Especially ones corrupted by Chaos, which is an actual thing, as the poor saps at the Battle for Calth found out.
Not to be confused with Logitator.
The most common type of Cogitator, Dataslates are basically tablets with black and green screens, word processor programs and maybe a few more basic functions to handle the paperwork of the Imperium. Basically they are Tablets or a 40k version of the PADD from Star_Trek