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Is \( \mathcal{P}\mathcal{L}_2 \) a Tractable Language?

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Progress in Artificial Intelligence (EPIA 1999)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 1695))

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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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Author information

Authors and Affiliations

  1. Departamento de Informática Faculdade de Ciências e Tecnologia, Universidade Nova de Lisboa, 2825-114, Caparica, Portugal

    Aida Vitória & Margarida Mamede

Authors
  1. Aida Vitória
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  2. Margarida Mamede
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Editors and Affiliations

  1. Departamento de Informática, Universidade Nova de Lisboa, Quinta da Torre, P-2825-114, Caparica, Portugal

    Pedro Barahona

  2. Departamento de Matemática, Universidade de Évora, R. Romão Ramalho 59, P-7000, Évora, Portugal

    José J. Alferes

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© 1999 Springer-Verlag Berlin Heidelberg

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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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  • Print ISBN: 978-3-540-66548-9

  • Online ISBN: 978-3-540-48159-1

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