Complexity Boundaries for Horn Description Logics

Horn description logics (Horn-DLs) have recently started to attract attention due to the fact that their (worst-case) data complexities are in general lower than their overall (i. e. combined) complexities, which makes them attractive for reasoning with large ABoxes. However, the natural question whether Horn-DLs also provide advantages for TBox reasoning has hardly been addressed so far. In this paper, we therefore provide a thorough and comprehensive analysis of the combined complexities of Horn-DLs. While the combined complexity for many Horn-DLs turns out to be the same as for their non-Horn counterparts, we identify subboolean DLs where Hornness simplifies reasoning.

Authors

• Markus Krötzsch

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