Are you talking about base suppositions about truth tables or truth tables in themselves. What I mean is, are the classes you list (i.e. tautology, etc.) master categories of the established rules (i.e. conjunction, disjunction, etc.)
like instead of taking the basic truth tables as is, you suppose there is a grander scale. so instead of saying;
you would suppose that these would come after the classifications you list (i.e tautology, etc.) so it would looks something like this (the x means one of the classifications you suppose)
* (x) -- > conjunction
* (x) -- > disjunction
* (x) -- > conditional
* (x) -- > biconditional
More elaboration please!