Modal Logics for Reasoning about Preferences and Cooperation: Expressive Power and Complexity
Cédric Dégremont, Lena Kurzen
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.