Modal Logics with Counting

C. Areces, G. Hoffmann, and A. Denis. Modal Logics with Counting. In WoLLIC 2010 17th Workshop on Logic, Language, Information and Computation - WoLLIC 2010, Brasilia, Brazil, 2010.

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Abstract

We present a modal language that includes explicit operators to count the number of elements that a model might include in the extension of a formula, and we discuss how this logic has been previously investigated under different guises. We show that the language is related to graded modalities and to hybrid logics. We illustrate a possible application of the language to the treatment of plural objects and queries in natural language. We investigate the expressive power of this logic via bisimulations, discuss the complexity of its satisfiability problem, define a new reasoning task that retrieves the cardinality bound of the extension of a given input formula, and provide an algorithm to solve it.

BibTeX

@InCollection{Areces2010a,
  author =       "C. Areces and G. Hoffmann and A. Denis",
  booktitle =    "{W}o{LLIC} 2010 17th {W}orkshop on {L}ogic,
                 {L}anguage, {I}nformation and {C}omputation -
                 {W}o{LLIC} 2010",
  title =        "Modal Logics with Counting",
  year =         "2010",
  address =      "{B}rasilia, {B}razil",
  abstract =     "We present a modal language that includes explicit
                 operators to count the number of elements that a model
                 might include in the extension of a formula, and we
                 discuss how this logic has been previously investigated
                 under different guises. We show that the language is
                 related to graded modalities and to hybrid logics. We
                 illustrate a possible application of the language to
                 the treatment of plural objects and queries in natural
                 language. We investigate the expressive power of this
                 logic via bisimulations, discuss the complexity of its
                 satisfiability problem, define a new reasoning task
                 that retrieves the cardinality bound of the extension
                 of a given input formula, and provide an algorithm to
                 solve it.",
  keywords =     "{M}odal logics ; {C}ounting",
  ISBN =         "978-3-642-13823-2",
}