During the past forty years the term "quantum logic" has been used with many different meanings and even today one has to distinguish between a large number of differing concepts of "quantum logic". A survey of the various interpretations of this expression can be found, for example, in the proceedings of a recent conference on "Current Issues in Quantum Logic".1 Due to this great ambiguity of the term "quantum logic" it seems necessary first to clarify what is meant precisely by "quantum logic" in this article. Here we consider a formal object language, the elementary pro positions of which are concerned with the present state and the temporal development of real physical objects. If this abstract language of physics describes objects that belong to that part of the physical reality which is governed by the laws of "classical physics" we call it C-language or 5^c. If, in addition, the language incorporates also propositions about physical objects which belong to the domain of "quantum physics", then this more universal language will be called O-language, or 6^0. The most abstract syntactical structure of this language 5^0, i.e., the formal logic of O-language, will be denoted as "quantum logic" or Q-logic. Analogously we call the formal logic of the more special language 6^c of classical physics C-logic. Whether the distinction between C-language and O-language and between C-logic and O-logic respectively is actually relevant will be discussed in the following sections. This explication of the term "quantum logic" leaves the question still open, whether this formal logic of quantum language can be justified by a priori reasons or whether it can be obtained solely from experience. Irrespective of the answer to this question, it is obvious that "quantum logic" represents some intrinsic structure of the physical reality which can be discovered at least in principle from physical observations or from a corresponding physical theory. Starting from the empirically well established quantum theory in Hilbert space, G. Birkhoff and J.v.