Computational theory is based on information states and actions. This works quite well within a Turing machine framework and is well defined with lambda calculus. The programming language, LISP is based on lambda calculus.
Cognitive theory is quite different because it is based on motivation, inhibition, and comprehension. When you try to combine these two together you end up with problems. This is described reasonably well by Dennett here:
http://web.fc.uaem.mx/~bruno/material/dennet_93_cognitiveWheels.pdf
In cognitive theory, any data pattern can be abstracted to cause an action. If you've played Monopoly you have cards which have actions on them like "Go to Jail" or "Go to the Reading Railroad". So, separate the patterns from the actions. For example, you could roll dice or choose a card from a standard deck and then look up the action in a table. Now, if you can have a card that represents an action then you could also use an environmental pattern. When the robot sees pattern X, it runs through the look up table and does whatever is listed in the table. This doesn't require any comprehension, only pattern recognition and a table of actions. So, everything is wonderful. Except it isn't because eventually the table becomes so large that it takes too long to look up anything. This is the tongue-in-cheek description by Dennett about a robot taking too long to figure out a solution.
I understood this problem many years ago when I wrote programs in Prolog which is based on predicate calculus. In fact, this was tried and failed miserably. The closest anyone has gotten to this is
IBM's Watson which played on the show, Jeopardy. This too is a miserable failure. Although I suppose many would claim that it is a success in terms of being a natural language interface to a an expert system. In this respect it is related to things like Siri. Most people are aware that Siri has rather legendary problems with comprehension.
Basically, the die-hard Computational Theorists claim that Motivation, Inhibition, and Comprehension can be simulated however this rather misses the point. Cognitive theory requires general solutions based on broad abstraction. In contrast, cognitive theory relies on external abstraction protocols which have never had a general solution. So, can you create general solutions without adding yet another rule every time the computer makes a mistake? Computational theorists would like to say, yes. Based on what I know about Cognitive theory I would say this cannot be done within the framework of a Turing machine.