By using the residual implication on a frame L, we develop a theory of separation axioms in the category of stratified L-generalized convergence spaces in the spirit of Lowen, i.e., we define for each space some degrees of fulfilling T 0 , T 1 , T 2 and regularity axioms from a logical aspect. These degrees of separation axioms generalize the theory of separation axioms in the sense of Jäger.