PP-2008-39: Modal Logics for Reasoning about Preferences and Cooperation: Expressive Power and Complexity

PP-2008-39: Dégremont, Cédric and Kurzen, Lena (2008) Modal Logics for Reasoning about Preferences and Cooperation: Expressive Power and Complexity. [Report]

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Abstract

This paper gives a survey of expressivity and complexity of normal modal logics for reasoning about cooperation and preferences. We identify a class of notions expressing local and global properties rel- evant for reasoning about cooperative situations involving agents that have preferences. Many of these notions correspond to game- and social choice-theoretic concepts. We specify what expressive power is required for expressing these notions. This is done 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 lan- guages is specified and we show how the chosen notions can be expressed in fragments of this class. In order to determine how demanding reason- ing 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.

Item Type: Report
Report Nr: PP-2008-39
Series Name: Prepublication (PP) Series
Year: 2008
Uncontrolled Keywords: Modal Logic; Cooperation; Preferences; Expressive power; Computational Complexity
Date Deposited: 12 Oct 2016 14:37
Last Modified: 12 Oct 2016 14:37
URI: https://eprints.illc.uva.nl/id/eprint/313

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