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Modal Logics with Counting

  • Conference paper
Logic, Language, Information and Computation (WoLLIC 2010)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 6188))

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.

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Author information

Authors and Affiliations

  1. INRIA Nancy Grand Est, France

    Carlos Areces, Guillaume Hoffmann & Alexandre Denis

Authors
  1. Carlos Areces
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  2. Guillaume Hoffmann
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  3. Alexandre Denis
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Editor information

Editors and Affiliations

  1. Computer Laboratory, University of Cambridge, J.J. Thomson Avenue, CB3 0FD, Cambridge, UK

    Anuj Dawar

  2. Centro de Informática, Universidade Federal de Pernambuco, Avenida Prof Luis Freire s/n, Cidade Universitária, 50740-540, Recife, PE, Brazil

    Ruy de Queiroz

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Areces, C., Hoffmann, G., Denis, A. (2010). Modal Logics with Counting. In: Dawar, A., de Queiroz, R. (eds) Logic, Language, Information and Computation. WoLLIC 2010. Lecture Notes in Computer Science(), vol 6188. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-13824-9_9

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  • DOI: https://doi.org/10.1007/978-3-642-13824-9_9

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-13823-2

  • Online ISBN: 978-3-642-13824-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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