Knowing that one knows and the classical definition of knowledge

In his Essay in Modal Logic, G. H. von Wright suggested that the logic of knowledge or epistemic logic is a branch of modal logic.1 E. J. Lemmon has recommended a system of epistemic logic based on the Feys-von Wright modal system M,2 and in Knowledge and Belief Jaakko Hintikka proposed a stronger system which corresponds to Lewis's S4.3 The distinctive axiom of S4 is 'Np^NNp',* and the epistemic counter part of this formula is the principle that knowing implies knowing that one knows, that is,