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Modal Logics for Preferences and Cooperation: Expressivity and Complexity

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Knowledge Representation for Agents and Multi-Agent Systems (KRAMAS 2008)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 5605))

Abstract

This paper studies expressivity and complexity of normal modal logics for reasoning about cooperation and preferences. We identify a class of local and global notions relevant for reasoning about cooperation of agents that have preferences. Many of these notions correspond to game- and social choice-theoretical concepts. We specify the expressive power required to express these notions by determining whether they are invariant under certain relevant operations on different classes of Kripke models and frames. A large class of known extended modal languages is specified and we show how the chosen notions can be expressed in fragments of this class. To determine how demanding reasoning about cooperation is in terms of computational complexity, we use known complexity results for extended modal logics and obtain for each local notion an upper bound on the complexity of modal logics expressing it.

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Authors and Affiliations

  1. Universiteit van Amsterdam,  

    Cédric Dégremont & Lena Kurzen

Authors
  1. Cédric Dégremont
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  2. Lena Kurzen
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Editors and Affiliations

  1. Department of Information and Computing Sciences, Universiteit Utrecht, Centrumgebouw Noord, Office A123, Padualaan 14, De Uithof, 3584, Utrecht, CH, The Netherlands

    John-Jules Ch. Meyer

  2. Department of Information and Computing Sciences, Universiteit Utrecht, Centrumgebouw Noord, Office A122, Padualaan 14, De Uithof, 3584, Utrecht, CH, The Netherlands

    Jan Broersen

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Dégremont, C., Kurzen, L. (2009). Modal Logics for Preferences and Cooperation: Expressivity and Complexity. In: Meyer, JJ.C., Broersen, J. (eds) Knowledge Representation for Agents and Multi-Agent Systems. KRAMAS 2008. Lecture Notes in Computer Science(), vol 5605. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-05301-6_3

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  • DOI: https://doi.org/10.1007/978-3-642-05301-6_3

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-05300-9

  • Online ISBN: 978-3-642-05301-6

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