  The present paper develops a unified correspondence treatment of the
Sahlqvist theory for possibility semantics, extending the results in
\cite{Ya16} from Sahlqvist formulas to the strictly larger class of inductive
formulas, and from the full possibility frames to filter-descriptive
possibility frames. Specifically, we define the possibility semantics version
of the algorithm ALBA, and an adapted interpretation of the expanded modal
language used in the algorithm. We prove the soundness of the algorithm with
respect to both (the dual algebras of) full possibility frames and (the dual
algebras of) filter-descriptive possibility frames. We make some comparisons
among different semantic settings in the design of the algorithms, and fit
possibility semantics into this broader picture.
  One notable feature of the adaptation of ALBA to possibility frames setting
is that the so-called nominal variables, which are interpreted as complete
join-irreducibles in the standard setting, are interpreted as regular open
closures of "singletons" in the present setting.
