 and calling # congruential according to ⊢ when # is congruential in each of its positions according to ⊢. Clearly a consequence relation is congruential in the sense of Section  1—which  of course also makes sense for generalized consequence relations—precisely when each primitive connective in its language is congruential in every position according to it. A similar lifting of properties of connectives—‘according to’ (generalized) consequence relations—can be made in the other cases too, for example calling a consequence relation fully determined when each of the primitive connectives of its language is fully determined according to it. Thus we may say that the consequence relation ⊢CL of classical logic (with any given stock of primitive connectives—though we will not further decorate the notation to indicate a particular fragment) is fully determined and thus also extensional (and congruential), while the consequence relation ⊢I L of intuitionistic logic is congruential but not extensional, since for example, ¬, is not right-extensional according to ⊢I L. The consequence relation determined by the well-known three-element matrix of Łukasiewicz is not even congruential, since (again) ¬ is not congruential according to this relation. There is a weaker property than extensionality as here defined (for the sake of the above connection with pseudo-truth-functionality) which properly implies left extensionality but not right extensionality and which, unlike left extensionality itself, implies congruentiality. We could define #, here taken for illustrative purposes again as 1-ary, to be weakly extensional according to a consequence relation ⊢ when for all Γ, φ, ψ: