  This work builds upon a well-established research tradition on modal logics
of awareness. One of its aims is to export tools and techniques to other areas
within modal logic. To this end, we illustrate a number of significant bridges
with abstract argumentation, justification logics, the epistemic logic of
knowing-what and deontic logic, where basic notions and definitional concepts
can be expressed in terms of the awareness operator combined with the box
modality. Furthermore, these conceptual links point to interesting properties
of awareness sets beyond those standardly assumed in awareness logics, i.e.
positive and negative introspection. We show that the properties we list are
characterised by corresponding canonical formulas, so as to obtain a series of
off-the-shelf axiomatisations for them. As a second focus, we investigate the
general dynamics of this framework by means of event models. Of specific
interest in this context is to know under which conditions, given a model that
satisfies some property, the update with an event model keeps it within the
intended class. This is known as the closure problem in general dynamic
epistemic logics. As a main contribution, we prove a number of closure theorems
providing sufficient conditions for the preservation of our properties. Again,
these results enable us to axiomatize our dynamic logics by means of reduction
axioms.
