A logic-algebraic framework for contextuality and modality in quantum systems

In this work we develop a modal structure for the simultaneous treatment of actual and possible properties of quantum systems. A logical system based on orthomodular lattices enriched with a modal operator is given, obtaining algebraic completeness and completeness with respect to a Kripke-style semantic. We show that, in spite of the fact that, the language is enriched with the addition of a modal operator, contextuality remains a central feature of quantum systems