Modal Logics for Preferences and Cooperation: Expressivity and Complexity

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.