We study access to temporal data with TEL, a temporal extension of the tractable description logic EL. Our aim is to establish a clear computational complexity landscape for the atomic query answering problem, in terms of both data and combined complexity. Atomic queries in full TEL turn out to be undecidable even in data complexity. Motivated by the negative result, we identify well-behaved yet expressive fragments of TEL. Our main contributions are a semantic and sufficient syntactic conditions for decidability and three orthogonal tractable fragments, which are based on restricted use of rigid roles, temporal operators, and novel acyclicity conditions on the ontologies
