I have here an entirely unrelated, incompatible version of socionics.
It has always seemed odd to me that thinking opposes feeling and sensing opposes intuition. This implies that T/F are somehow capable of doing the same jobs, as are S/N. However, from my own observations, it seems more common that T/N are more likely to do the same jobs, as are S/F. T/N both deal in highly processed information, taking what is already known and refining it. "Oh, it all fits into a pattern," or "If X is true and Y is true, Z must be false." S/F make judgements (in the colloquial sense) about various things and ideas out of nothing. "This is comfortable," "I want that," or "That is morally wrong." These ideas, though valid, don't come from anywhere - the function throws them forward automatically, and the reasoning behind them cannot really be explained, only rationalized. In contrast, I don't see how T/N can really have any desires or goals in themselves. Even the desire to accumulate knowledge has to originate from somewhere - desire cannot be deduced. A pure NT would probably mope around in a lifelong existentialist stupor.
Thus, let's try dividing the functions into Abstract/Involved, rather than Judging/Perceiving. Everyone relies upon one abstract function and one involved function of opposite attitude, like ISE, LSI, or ELI.
Seems like a reasonable system?
What's your A/I Socionics type?