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Capturing Stationary and Regular Extensions with Reiter’s Extensions

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Logics in Artificial Intelligence (JELIA 2000)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 1919))

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Abstract

Janhunen et al. [14] have proposed a translation technique for normal logic programs in order to capture the alternating fix-points of a program with the stable models of the translation. The same technique is also applicable in the disjunctive case so that partial stable models can be captured. In this paper, the aim is to capture Przymusinska and Przymusinski’s stationary extensions with Reiter’s extensions using the same translational idea. The resulting translation function is polynomial, but only weakly modular and not perfectly faithful. Fortunately, another technique leads to a polynomial, faithful and modular (PFM) translation function. As a result, stationary default logic (STDL) is ranked in the expressive power hierarchy (EPH) of non-monotonic logics [13]. Moreover, reasoning with stationary extensions as well as brave reasoning with regular extensions (i.e., maximal stationary extensions) can be implemented using an inference engine for reasoning with Reiter’s extensions.

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Author information

Authors and Affiliations

  1. Laboratory for Theoretical Computer Science, Helsinki University of Technology, P.O.Box 5400, FIN-02015 HUT, Finland

    Tomi Janhunen

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  1. Tomi Janhunen
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Editor information

Editors and Affiliations

  1. Department of Applied Mathematics, E.T.S.I. Informática, University of Málaga, 29071, Málaga, Spain

    Manuel Ojeda-Aciego  & Inma P. de Guzmán  & 

  2. Intelligent Systems Department, Computer Science Institute, University of Leipzig, Augustusplatz 10-11, 04109, Leipzig, Germany

    Gerhard Brewka

  3. Center for Artificial Intelligence, Department of Computer Science, University of Lisbon, 2825-114, Caparica, Portugal

    Luís Moniz Pereira

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© 2000 Springer-Verlag Berlin Heidelberg

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Janhunen, T. (2000). Capturing Stationary and Regular Extensions with Reiter’s Extensions. In: Ojeda-Aciego, M., de Guzmán, I.P., Brewka, G., Moniz Pereira, L. (eds) Logics in Artificial Intelligence. JELIA 2000. Lecture Notes in Computer Science(), vol 1919. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-40006-0_8

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  • DOI: https://doi.org/10.1007/3-540-40006-0_8

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  • Print ISBN: 978-3-540-41131-4

  • Online ISBN: 978-3-540-40006-6

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