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Hello.
The concepts of basis and superstructure are related to such concepts as basic and derivative, axiom and theorem. In logic, the basis can be an axiom, and the superstructure can be a theorem. How are they related? A theorem is deduced (proved) from the axiom, and hence it follows logically from it. On the other hand, the basic concept gives rise to a derived concept, which is defined on the basis of the basic concept. Unfortunately, now logic studies only taxonomic relations between concepts (by volume), but almost does not consider the question of relations by definition (which concept is defined with the help of another? or are they both defined from something third, common? sometimes, on the contrary, the third is determined immediately on the basis of two data).
In general, we go from the basis to the superstructure by some operation (definition, inference, etc.). Sometimes the superstructure is distinguished as a result (what happened), and sometimes – as a change (to which step we moved, the step itself is considered as an add-on).
A lot of logic needs to be worked out. Mathematical logic is mainly concerned with the theory of inferences (proofs), while many other issues, such as this question, require the attention of scientists.