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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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
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