Open Answer Set Programming (OASP) is an undecidable framework for
integrating ontologies and rules. Although several decidable fragments of OASP
have been identified, few reasoning procedures exist. In this article, we
provide a sound, complete, and terminating algorithm for satisfiability
checking w.r.t. Forest Logic Programs (FoLPs), a fragment of OASP where rules
have a tree shape and allow for inequality atoms and constants. The algorithm
establishes a decidability result for FoLPs. Although believed to be decidable,
so far only the decidability for two small subsets of FoLPs, local FoLPs and
acyclic FoLPs, has been shown. We further introduce f-hybrid knowledge bases, a
hybrid framework where \SHOQ{} knowledge bases and forest logic programs
co-exist, and we show that reasoning with such knowledge bases can be reduced
to reasoning with forest logic programs only. We note that f-hybrid knowledge
bases do not require the usual (weakly) DL-safety of the rule component,
providing thus a genuine alternative approach to current integration approaches
of ontologies and rules
