It is shown that while the problem of deciding satisfiability of an S5 formula with one agent is NP-complete, the problem for many agents is PSPACE-complete and the problem becomes complete for exponential time once a common knowledge operator is added to the language.Expand

This second edition has been updated to reflect Halpern's recent research and includes a consideration of weighted probability measures and how they can be used in decision making.Expand

A language, CTL*, in which a universal or existential path quantifier can prefix an arbitrary linear time assertion, is defined and the expressive power of a number of sublanguages is compared.Expand

The automatic generation of adequate explanations, a task essential in planning, diag- nosis and natural language processing, therefore requires a formal analysis of the concept of actual cause, and a new deﬁnition of actual causes is proposed, using structural equations to model counterfac- tuals.Expand

In these logics, the set of beliefs of an agent does not necessarily contain all valid formulas, which makes them more suitable than traditional logics for modelling beliefs of humans (or machines) with limited reasoning capabilities.Expand

In certain areas of artificial intelligence there is need to represent continuous change and to make statements that are interpreted with respect to time intervals rather than time points. To this… Expand

We argue that the right way to understand distributed protocols is by considering how messages change the state of knowledge of a system. We present a hierarchy of knowledge states that a system may… Expand

This work provides axiom systems that are sound and complete in cases where a complete axiomatization is possible, and shows that they do allow us to capture a great deal of interesting reasoning about probability.Expand

K-resilient Nash equilibria, joint strategies where no member of a coalition C of size up to k can do better, even if the whole coalition defects, exist for secret sharing and multiparty computation, provided that players prefer to get the information than not to get it.Expand

This work provides a complete axiomatization for reasoning about knowledge and probability, proves a small model property, and obtains decision procedures for adding common knowledge and a probabilistic variant of common knowledge to the language.Expand