  This paper surveys some recent developments towards a dynamic quantum logic
and outlines its explicite construction -- some analogies and contrasts with
other logics of dynamics are indicated. Abstract: The development of ``(static)
operational quantum logic" points out that classical boolean structures are too
rigid to describe the actual and potential properties of quantum systems. On
the other hand, an intuitionistic perspective on operational quantum logic,
guides us in the direction of incorporating dynamics logically by reconsidering
the primitive propositions required to describe the behavior of a quantum
system, in particular in view of the emergent disjunctivity due to the
non-determinism of quantum measurements. A further elaboration on
"intuitionistic quantum logic" emerges into a "dynamic operational quantum
logic", which allows us to express dynamic reasoning in the sense that we can
capture how actual properties propagate, including their temporal causal
structure, and provides a unified logical description of systems which evolve
or which are submitted to measurements. This setting reveals that even static
operational quantum logic bears a hidden dynamic ingredient in terms of what is
called "the orthomodularity" of the lattice-structure. Focusing on the quantale
semantics for dynamic operational quantum logic, we delineate some points of
difference with the existing quantale semantics for (non)-commutative linear
logic.
