I recently began to wonder if a more logical program was more 'compatible' with the human mind, as in being more natural to use, and making the user feel more in control. Is this necessarily true? The reason I ask is because I am wondering if a simpler program is at all easier to use than one that takes the time but is more logical. Thank you for your time, any research/evidence is greatly appreciated, but do not feel entitled to present any.
I think what you mean is strongly related with the difference of the mental model of the user on how a system/program works and the experience the user has when expecting the behaviour of his/her mental model.
The term "logical" will be defined for each user a little bit different, based on knowledge, tech skills, experiences,...
So to make a program "logical" for the user, it is important, that the user is informed about what's going on (feedback, wizards, train the user), so his/her mental model of the system is close as possible to the actual systems model.
Further readings: NNorman Group - Mental Models and UX Design
If you are thinking logic that is adjusted to heuristics, then yes, because this will make a program predictable hence intuitive. But if you mean math logic, then no, it's counter-intuitive.