  Computation Tree Logic (CTL) and its extensions CTL* and CTL+ are widely used
in automated verification as a basis for common model checking tools. But while
they can express many properties of interest like reachability, even simple
regular properties like "Every other index is labelled a cannot be expressed in
these logics. While many extensions were developed to include regular or even
non-regular (e.g. visibly pushdown) languages, the first generic framework,
Extended CTL, for CTL with arbitrary language classes was given by Axelsson et.
al. and applied to regular, visibly pushdown and (deterministic) context-free
languages. We extend this framework to CTL* and CTL+ and analyse it with regard
to decidability, complexity, expressivity and satisfiability.
