To make informed decisions in a multiagent environment, an agent needs to model itself, the world, and the other agents, including the models that those other agents might be employing. We present a framework for recursive modeling that uses possible worlds semantics, and is based on extending the Kripke structure so that an agent can model the information it thinks that another agent has in ea...

Traditional results in modal logics state that, if a formula ' is satissable in K (K-satissable), then it has a Kripke model M s.t. jjM jj 2 j'j , jjM jj being the number of states of M and j'j the number of subformulas of '. A further result states a bound of jjM jj j'j d , d being the modal depth of '. In more recent papers, a decision procedure has been proposed which branches on the truth v...

We are interested in frame definability of classes of trees, using formulas of the μ-calculus. In this set up, the proposition letters (or in other words, the free variables) in the μ-formulas correspond to second order variables over which universally quantify. Our main result is a semantic characterization of the MSO definable classes of trees that are definable by a μ-formula. We also show t...