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Extending Paraconsistent \(\mathcal{SROIQ}\)

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Web Reasoning and Rule Systems (RR 2010)

Part of the book series: Lecture Notes in Computer Science ((LNISA,volume 6333))

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Abstract

The four-valued paraconsistent logic \(\mathcal{SROIQ}4\), originally presented by Ma and Hitzler, is extended to incorporate additional elements of \(\mathcal{SROIQ}\). It is shown that the modified logic is classically sound and that its embedding into classical \(\mathcal{SROIQ}\) is consequence preserving. Furthermore, inserting special axioms into a \(\mathcal{SROIQ}4\) knowledge base allows additional nontrivial conclusions to be drawn, without affecting paraconsistency. It is also shown that the interaction of nominals and cardinality restrictions prevents some \(\mathcal{SROIQ}4\) knowledge bases from having models. For such knowledge bases, the logic remains explosive.

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Author information

Authors and Affiliations

  1. Kno.e.sis Center, Wright State University,  

    Frederick Maier

Authors
  1. Frederick Maier
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Editor information

Editors and Affiliations

  1. Dept. of Computer Science and Engineering, Wright State University, 3640 Colonel Glenn Hwy, 45435, Dayton, OH, USA

    Pascal Hitzler

  2. Computing Laboratory, Oxford University, Wolfson Building, Parks Road, OX1 3QD, Oxford, UK

    Thomas Lukasiewicz

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Maier, F. (2010). Extending Paraconsistent \(\mathcal{SROIQ}\) . In: Hitzler, P., Lukasiewicz, T. (eds) Web Reasoning and Rule Systems. RR 2010. Lecture Notes in Computer Science, vol 6333. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-15918-3_10

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  • DOI: https://doi.org/10.1007/978-3-642-15918-3_10

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-15917-6

  • Online ISBN: 978-3-642-15918-3

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