Orthomodular logic. A proposal of a logic for quantum physics

Abstract

Classical physics are widely known to be closely related to classical propositional calculus, whereas there does not exist a strongly settled analogue for quantum physics. We will focus on orthomodular logic and, in particular, we will study two different sentential logics that have been purposed with this aim over othomodular lattices. Thus, we will introduce their semantics from the foundations of quantum mechanics and presenting them by means of two different approaches whose equivalence will be shown. Additionally, we will give an adequate syntax for each proposal, the first one due to M. L. dalla Chiara and R. Giuntini and the last one to G. Kalmbach. Finally, completeness theorems will be discussed as well as the results that have been reached.