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International Workshop on Information Search, Integration, and Personalization

ISIP 2012: Information Search, Integration and Personalization pp 131–140Cite as

Graded Modal Logic GS5 and Itemset Support Satisfiability

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Part of the book series: Communications in Computer and Information Science ((CCIS,volume 146))

Abstract

Graded modal logic GS5 is an extension of S5 by the modal connective \(\diamondsuit_\lambda\): the formula \(\diamondsuit_\lambda A\) means that there are at least λ worlds satisfying A. In this paper, we show how to reduce GS5 satisfiability to propositional satisfiability (SAT). Furthermore, we consider a satisfiability problem related to the frequent itemset mining problem: SUPPSAT n (where n is a strictly positive integer). We show how SUPPSAT n can be encoded in GS5 satisfiability and consequently in SAT.

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Author information

Authors and Affiliations

  1. Université Lille-Nord de France, France

    Yakoub Salhi, Saïd Jabbour & Lakhdar Sais

  2. CNRS UMR 8188, CRIL, Artois, F-62307, Lens, France

    Yakoub Salhi, Saïd Jabbour & Lakhdar Sais

Authors
  1. Yakoub Salhi
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  2. Saïd Jabbour
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  3. Lakhdar Sais
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Editor information

Editors and Affiliations

  1. Meme Media Laboratory, Hokkaido University, Sapporo, Japan

    Yuzuru Tanaka

  2. Laboratoire de Recherche en Informatique, Université Paris-Sud 11, France

    Nicolas Spyratos

  3. Hokkaido University, Sapporo, Japan

    Tetsuya Yoshida

  4. National Research Council, Istituto di Scienza e Tecnologie dell’Informazione, Pisa, Italy

    Carlo Meghini

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Salhi, Y., Jabbour, S., Sais, L. (2013). Graded Modal Logic GS5 and Itemset Support Satisfiability. In: Tanaka, Y., Spyratos, N., Yoshida, T., Meghini, C. (eds) Information Search, Integration and Personalization. ISIP 2012. Communications in Computer and Information Science, vol 146. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-40140-4_14

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  • DOI: https://doi.org/10.1007/978-3-642-40140-4_14

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-40139-8

  • Online ISBN: 978-3-642-40140-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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