Graded Modal Logic GS5 and Itemset Support Satisfiability

  • Yakoub Salhi
  • Saïd Jabbour
  • Lakhdar Sais
Conference paper
Part of the Communications in Computer and Information Science book series (CCIS, volume 146)


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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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Yakoub Salhi
    • 1
    • 2
  • Saïd Jabbour
    • 1
    • 2
  • Lakhdar Sais
    • 1
    • 2
  1. 1.Université Lille-Nord de FranceFrance
  2. 2.CNRS UMR 8188CRILLensFrance

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