  In this paper we present the fundamentals of the so-called algebraic approach
to propositional quantum logics. We define the set of formulas describing
quantum reality as a free algebra freely generated by the set of quantum
propositional variables. We define the general notion of logic as a structural
consequence operation. Next we introduce the concept of logical matrices
understood as a models of quantum logics. We give the definitions of two
quantum consequence operations defined in these models.
