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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.

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    I am glad you didn't use the word 'intuitive', because I think it is a quality that depends on the specific type of person. I feel like the terms 'simple' and 'logical' refer to two different aspects of software design (i.e. you can design a simple and logical program or a simple and illogical program). For me simplicity is about the number of moving parts and logic is about the way the parts connect together. – Michael Lai Jan 7 '15 at 3:55
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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

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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.

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