A New Approach to Quantum Logic - Dov M. Gabbay - Bog

This monograph is an investigation into certain new logical structures implicit in the formalism of quantum mechanics.
Its message rests on two pillars. The first pillar is the dynamic view of propositions. Propositions are viewed as acting on states of the world and changing them rather than just being true or false in them. The second pillar is a logical enquiry into the nature of the states of a dynamic framework in general and thus the nature of physical states in particular. It turns out that a physical state viewed as a logical entity must encode other states and also itself.
The main logical structures under investigation are that of an M-algebra and that of a holistic logic. In a sense to be made precise the latter structures reflect the 'holistic' nature of quantum mechanics.