I have said before in some posts that I am inclined to think that the J/P dichotomy is very important. Jung took his starting point at E/I, Keirsey takes off at S/N, but if we start from J/P we will be able to start from something that is observable. I believe that it also reflects a fundamental difference in attitude towards life. J and P types have different world views in a sense (Lenore Thomson has written something about this). And that difference can be seen and it can be felt when you interact with people.

One theory is that what people think of as J and P behaviors map to rational/irrational. The other theory (put forth both in MBTI and in the Socionics quadra descriptions) is that personalities with a Ti or Fi structure are P and those with a Te or Fe structure are J.
This is slightly inaccurate. Both Socionics and MBTI think that J and P behaviors map to rational/irrational, if we refer to the types as whole units. There is no other theory since what MBTI says about personalities with a Ti or Fi structure is not that different from what Socionics says about them. The way an INTP thinks is described the same way in MBTI as an INTp's way of thinking is described in Socionics. They use different words (like Ti and Ne in contrast to and ) to refer to the same empirical reality.