  We obtain modal completeness of the interpretability logics ILP_0 and ILR
w.r.t. generalized Veltman semantics. Our proofs are based on the notion of
smart (full) labels. We also give shorter proofs of completeness w.r.t.
generalized semantics for many classical interpretability logics. We obtain
decidability and finite model property w.r.t. generalized semantics for ILP_0
and ILR. Finally, we develop a construction that might be useful for proofs of
completeness of extensions of ILW w.r.t. generalized semantics in the future,
and demonstrate its usage with ILW* = ILM_0W.
