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A Guide to Completeness and Complexity for Modal Logics of Knowledge and Belief
TLDR
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
Reasoning about uncertainty
TLDR
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
“Sometimes” and “not never” revisited: on branching versus linear time temporal logic
TLDR
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
Causes and explanations: A structural-model approach
TLDR
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
Belief, Awareness, and Limited Reasoning.
TLDR
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
A propositional modal logic of time intervals
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 thisExpand
Knowledge and common knowledge in a distributed environment
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 mayExpand
An Analysis of First-Order Logics of Probability
TLDR
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
Distributed computing meets game theory: robust mechanisms for rational secret sharing and multiparty computation
TLDR
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
Reasoning about knowledge and probability
TLDR
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
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