Since the development of Notation3 Logic, several years have
passed in which the theory has been refined and used in practice by different reasoning engines such as cwm, FuXi or EYE. Nevertheless, a clear model-theoretic definition of its semantics is still missing. This leaves room for individual interpretations and renders it difficult to make clear
statements about its relation to other logics such as DL or FOL or even about such basic concepts as correctness. In this paper we address one of the main open challenges: the formalization of implicit quantification.
We point out how the interpretation of implicit quantifiers differs in two of the above mentioned reasoning engines and how the specification, proposed in the W3C team submission, could be formalized. Our formalization is then put into context by integrating it into a model-theoretic definition of the whole language. We finish our contribution by arguing why universal quantification should be handled differently than currently