  Modern logics of dependence and independence are based on team semantics,
which means that formulae are evaluated not on a single assignment of values to
variables, but on a set of such assignments, called a team. This leads to high
expressive power, on the level of existential second-order logic. As an
alternative, Baltag and van Benthem have proposed a local variant of dependence
logic, called logic of functional dependence (LFD). While its semantics is also
based on a team, the formulae are evaluated locally on just one of its
assignments, and the team just serves as the supply of the possible assignments
that are taken into account in the evaluation process. This logic thus relies
on the modal perspective of generalized assignments semantics, and can be seen
as a fragment of first-order logic. For the variant of LFD without equality,
the satisfiability problem is decidable.
  We extend the idea of localising logics of dependence and independence in a
systematic way, taking into account local variants of standard atomic
dependency properties: besides dependence and independence, also inclusion,
exclusion, and anonymity. We study model-theoretic and algorithmic questions of
the localised logics, and also resolve some of the questions that had been left
open by Baltag and van Benthem. In particular, we study decidability issues of
the local logics, and prove that satisfiability of LFD with equality is
undecidable. Further, we establish characterisation theorems via appropriate
notions of bisimulation and study the complexity of model checking problems for
these logics.
