There are 15 type dichotomies. Combining any two of these dichotomies creates a small group, such as quadra, temperament or club. Every small group is defined by 3 dichotomies and by selecting two traits, you select the small group and imply what the third trait must be.
For example, the Linear Assertive temperament consist of the four types that are extroverted, rational and dynamic: LIE, EIE, LSE, ESE. I can refer to this temperament as extroverted + rational types, extroverted + dynamic types or rational + dynamic types. Either way, I am always talking about the Ej temperament, and by extension, the third trait I did not use.
Since these three traits are dependent on each other, you can create impossible combinations. If all extroverted + rational types are dynamic, then there are no types that are say, extroverted + rational + static. You can use this property as a parity check and check for errors.
The only type that is static+ positivist+tactical+asking is ILE. ILE is a constructivist, not an emotivist. That's why that type combination doesn't work. Not that we know this person is ILE. All dichotomies being equally reliable, ILE, SEE, IEI and LSI are all the most likely.
I have an excel program I made showing this structure if you are a visual person.