We continue with the task of obtaining a unifying view of process semantics
by considering in this case the logical characterization of the semantics. We
start by considering the classic linear time-branching time spectrum developed
by R.J. van Glabbeek. He provided a logical characterization of most of the
semantics in his spectrum but, without following a unique pattern. In this
paper, we present a uniform logical characterization of all the semantics in
the enlarged spectrum. The common structure of the formulas that constitute all
the corresponding logics gives us a much clearer picture of the spectrum,
clarifying the relations between the different semantics, and allows us to
develop generic proofs of some general properties of the semantics.