Quantum logics and Lindenbaum property

This paper will take into account the Lindenbaum property in Orthomodular Quantum Logic (OQL) and Partial Classical Logic (PCL). The Lindenbaum property has an interest both from a logical and a physical point of view since it has to do with the problem of the completeness of quantum theory and with the possibility of extending any semantically non-contradictory set of formulas to a semantically non-contradictory complete set of formulas. The main purpose of this paper is to show that both OQL and PCL cannot satisfy the Lindenbaum property.I would like to thank Dr. P. L. Minari and Dr. G. Corsi for many enlightening and encouraging conversations. I am especially grateful to Prof. M. L. Dalla Chiara who sparked my interest in Quantum Logic and Philosophy of Physics.