Theories in propositional logiс and the converse of substitution

The paper considers the question of the existence and number of substitutional logics. It is proved that every tabular logic with a functionally complete system of connectives is substitutional. For these logics, the existence of an algorithm is proved, which, for a recursive consistent axiomatic of the theory, constructs an exact unifying substitution for it. A countable set of substitutional tabular logics is constructed. Some substitutional tabular logics with meaningful interpretation are presented. In addition, it is proved that every substitutional logic has a characteristic matrix. It is proved that there are continuum of nonsubstitutional logics.