Model-Theoretic Investigations into Consequence Operation (Cn) in   Quantum Logics. An Algebraic Approach
  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. 
Piotr Wilczek