Abstract
It is believed by the scientific community that \( \mathcal{P}\mathcal{L}_1 \) and \( \mathcal{P}\mathcal{L}_2 \) are the largest concept languages for which there exists a polynomial algorithm that solves the subsumption problem. This is due to Donini, Lenzerini, Nardi, and Nutt, who have presented two tractable algorithms that are intended to solve the subsumption problem in those languages. In contrast, this paper proves that the algorithm for checking subsumption of concepts expressed in the language \( \mathcal{P}\mathcal{L}_2 \) is not complete. As a direct consequence, it still remains an open problem to which computational complexity class this subsumption problem belongs.
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Vitória, A., Mamede, M. (1999). Is \( \mathcal{P}\mathcal{L}_2 \) a Tractable Language?. In: Barahona, P., Alferes, J.J. (eds) Progress in Artificial Intelligence. EPIA 1999. Lecture Notes in Computer Science(), vol 1695. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48159-1_7
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DOI: https://doi.org/10.1007/3-540-48159-1_7
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