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Data Complexity in the EL family of DLs

In recent years, lightweight description logics (DLs) have experienced increased interest because they admit highly efficient reasoning on large-scale ontologies. Most prominently, this is witnessed by the ongoing research on the DL-Lite and EL families of DLs, but see also [11, 14] for other examples. The main application of EL and its relatives is as an ontology language [5, 1, 3]. In particular, the DL EL proposed in [1] admits tractable reasoning while still providing sufficient expressive power to represent, for example, life-science ontologies. In contrast, the DL-Lite family of DLs is specifically tailored towards data intensive applications [8, 6, 7]. In such applications, instance checking and conjunctive query answering are the most relevant reasoning tasks and should thus be computationally cheap, preferably tractable. When determining the computational complexity of these task for a given DL, it is often realistic to consider data complexity, where the size of the input is measured only in terms of the ABox (which represents the data and tends to be large), but not in terms of the TBox and the query concept (which tend to be comparatively small). This is in contrast to combined complexity, where also the size of the TBox and query concept are taken into account.