Propositions and orthocomplementation in quantum logic

We briefly analyze two partial order relations that are usually introduced in quantum logic by making use of the concepts of yes-no experiment and of preparation as fundamental. We show that two distinct posetsE andL can be defined, the latter being identifiable with the lattice of quantum logic. We consider the posetE and find that it contains a subsetE ₀ which can easily be orthocomplemented. These results are used, together with suitable assumptions, in order to show that an Orthocomplementation inL can be deduced by the Orthocomplementation defined inE ₀, and also to give a rule to find the orthocomplement of any element ofL.Research sponsored by C.N.R. (Italy).