On epistemic logic and logical omniscience
Proceedings of the 1986 Conference on Theoretical aspects of reasoning about knowledge
On the complexity of epistemic reasoning
Proceedings of the Fourth Annual Symposium on Logic in computer science
A guide to completeness and complexity for modal logics of knowledge and belief
Artificial Intelligence
Reasoning about knowledge
Word problems requiring exponential time(Preliminary Report)
STOC '73 Proceedings of the fifth annual ACM symposium on Theory of computing
Symbolic Model Checking the Knowledge of the Dining Cryptographers
CSFW '04 Proceedings of the 17th IEEE workshop on Computer Security Foundations
Characterizing the NP-PSPACE gap in the satisfiability problem for modal logic
IJCAI'07 Proceedings of the 20th international joint conference on Artifical intelligence
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Fagin, Halpern, Moses, and Vardi have proposed a framework of epistemic agents with multiple "frames of mind" (local-reasoning structures), to solve problems concerning inconsistent knowledge and logical omniscience. We investigate a class of related modal logics. These logics replace the usual closure under full conjunction for the □ operator with progressively weaker versions, and comprise a hierarchy with the traditional modal logic K at the top, and an infinite number of logics ordered by inclusion under it, all strictly stronger than N, the weakest monotonic modal logic. Previous results have used N to represent local-reasoning structures. Our result shows that there are stronger logics applicable to such structures, suggesting that stronger forms of inference can be used to represent imperfect knowledge-based agents and protocols. Further, it is shown that the satisfiability question for each of these logics is PSPACE-complete, strictly harder than for N. This also answers a conjecture of Vardi: the border between NP- and PSPACE-hardness in modal-logical satisfiability problems is associated with conjunctive closure, however weak.