Modal Logics for Reasoning about Preferences and Cooperation: Expressivity and Complexity

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 relevant for reasoning about cooperative situations involving agents that have preferences. Many of these notions correspond to gameand 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 languages is specified and we show how the chosen notions can be expressed in fragments of this class. In order 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.