The paper introduces a worst-case optimal tableau algorithm for reasoning with Forest Logic Programs, a decidable fragment of Open Answer Set Programming. FoLPs are a useful device for tight integration of the Description Logic and the Logic Programming worlds: reasoning with the DL SHOQ can be simulated within the fragment. The algorithm reuses a knowledge compilation technique previously introduced, but improves on previous results by decreasing the worst-case running time with one exponential level. The decrease in complexity is due to the usage in conjunction of a new redundancy and of a new caching rule.

Combined approaches have become a successful technique for CQ answering over ontologies. Existing algorithms, however, are restricted to the logics underpinning the OWL 2 profiles. Our goal is to make combined approaches applicable to a wider range of ontologies. We focus on RSA: a class of Horn ontologies that extends the profiles while ensuring tractability of standard reasoning. We show that CQ answering over RSA ontologies without role composition is feasible in NP. Our reasoning procedure generalises the combined approach for ELHO and DL-LiteR using an encoding of CQ answering into fact entailment w.r.t. a logic program with function symbols and stratified negation. Our results have significant practical implications since many out-of-profile Horn ontologies are RSA.