On the complexity of epistemic reasoning
Proceedings of the Fourth Annual Symposium on Logic in computer science
Reasoning about knowledge
Modal logic
On epistemic logic and logical omniscience
TARK '86 Proceedings of the 1986 conference on Theoretical aspects of reasoning about knowledge
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In this article we discuss two alternative proposals for neighbourhood semantics (which we call strict and loose neighbourhood semantics, N= and N⊆ respectively) that have been previously introduced in the literature. Our main tools are suitable notions of bisimulation. While an elegant notion of bisimulation exists for N⊆, the required bisimulation for N= is rather involved. We propose a simple extension of N= with a universal modality that we call N=(E), which comes together with a natural notion of bisimulation. We also investigate the complexity of the satisfiability problem for N⊆ and N=(E).