Although being quite inexpressive, the description logic (DL) FL0, which provides only conjunction, value restriction and the top concept as concept constructors, has an intractable subsumption problem in the presence of terminologies (TBoxes): subsumption reasoning w.r.t. acyclic FL0 TBoxes is coNP-complete, and becomes even ExpTimecomplete in case general TBoxes are used. In the present paper, we use automata working on infinite trees to solve both standard and non-standard inferences in FL0 w.r.t. general TBoxes. First, we give an alternative proof of the ExpTime upper bound for subsumption in FL0 w.r.t. general TBoxes based on the use of looping tree automata. Second, we em- ploy parity tree automata to tackle non-standard inference problems such as computing the least common subsumer and the difference of FL0 concepts w.r.t. general TBoxes.

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Classical regular path queries (RPQs) can be too restrictive for some applications and answering such queries under approximate semantics to relax the query is desirable. While for answering regular path queries over graph databases under approximate semantics algorithms are available, such algorithms are scarce for the ontology-mediated setting. In this paper we extend an approach for answering RPQs over graph databases that uses weighted transducers to approximate paths from the query in two ways. The first extension is to answering approximate conjunctive 2-way regular path queries (C2RPQs) over graph databases and the second is to answering C2RPQs over ELH and DL-LiteR ontologies. We provide results on the computational complexity of the underlying reasoning problems and devise approximate query answering algorithms.