Data Complexity in the EL Family of Description Logics

We study the data complexity of instance checking and conjunctive query answering in the \(\mathcal{EL}\) family of description logics, with a particular emphasis on the boundary of tractability. We identify a large number of intractable extensions of \(\mathcal{EL}\), but also show that in \(\mathcal{ELI}^f\), the extension of \(\mathcal{EL}\) with inverse roles and global functionality, conjunctive query answering is tractable regarding data complexity. In contrast, already instance checking in \(\mathcal{EL}\) extended with only inverse roles or global functionality is ExpTime-complete regarding combined complexity.

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