Optimal nonrecursive datalog rewritings of linear TGDs and bounded (Hyper)Tree-width queries

Our concern is answering ontology-mediated queries (Ο q), whereΟ is a set of linear tgds and q a conjunctive query (CQ) of bounded hypertree width. Assuming that the arity of predicates is bounded, we show that polynomial-size nonrecursive Datalog rewritings can be constructed and executed in (i) LOGCFL for OMQs with ontologies of bounded existential depth; (ii) NL for OMQs with ontologies of bounded depth and CQs whose hypertree decompositions have a bounded number of leaves; (iii) LOGCFL for OMQs with acyclic CQs whose join trees have a bounded number of leaves