  We study probabilistic team semantics which is a semantical framework
allowing the study of logical and probabilistic dependencies simultaneously. We
examine and classify the expressive power of logical formalisms arising by
different probabilistic atoms such as conditional independence and different
variants of marginal distribution equivalences. We also relate the framework to
the first-order theory of the reals and apply our methods to the open question
on the complexity of the implication problem of conditional independence.
