  In the present article, we explore a new approach for the study of
orthomodular lattices, where we replace the problematic conjunction by a binary
operator, called the Sasaki projection. We present a characterization of
orthomodular lattices based on the use of an algebraic version of the Sasaki
projection operator (together with orthocomplementation) rather than on the
conjunction. We then define of a new logic, which we call Sasaki Orthologic,
which is closely related to quantum logic, and provide a rule-based definition
of this logic.
