Geodesic
On the Complexity of (Restricted) $\mathcal{ALCI}r$
Publications de l'Institut Mathématique, _N_S_95 (2014) no. 109, p. 133 .

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We consider a new description logic $\mathcal{ALCI}r$ that extends $\mathcal{ALCI}$ with role inclusion axioms of the form $R \sqsubseteq Q R_1 \dots R_m$ satisfying a certain regularity condition. We prove that concept satisfiability with respect to RBoxes in this logic is \ExpTime-hard. We then define a restriction $\mathcal{ALCI}r^-$ of $\mathcal{ALCI}r$ and show that concept satisfiability with respect to RBoxes in $\mathcal{ALCI}r^-$ is \PSpace-complete.
Classification : 68T27 03B70 68T30 68W40 68Q25 
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     author = {Milenko Mosurovi\'c and Michael Zakharyaschev},
     title = {On the {Complexity} of {(Restricted)} $\mathcal{ALCI}r$},
     journal = {Publications de l'Institut Math\'ematique},
     pages = {133 },
     publisher = {mathdoc},
     volume = {_N_S_95},
     number = {109},
     year = {2014},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/PIM_2014_N_S_95_109_a9/}
}
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Milenko Mosurović; Michael Zakharyaschev. On the Complexity of (Restricted) $\mathcal{ALCI}r$. Publications de l'Institut Mathématique, _N_S_95 (2014) no. 109, p. 133 . http://geodesic.mathdoc.fr/item/PIM_2014_N_S_95_109_a9/