All I know: a study in autoepistemic logic
Artificial Intelligence
A guide to completeness and complexity for modal logics of knowledge and belief
Artificial Intelligence
The expressive power of the hierarchical approach to modeling knowledge and common knowledge
TARK '92 Proceedings of the fourth conference on Theoretical aspects of reasoning about knowledge
What can machines know?: On the properties of knowledge in distributed systems
Journal of the ACM (JACM)
Levesque's axiomatization of only knowing is incomplete
Artificial Intelligence
MAAMAW '99 Proceedings of the 9th European Workshop on Modelling Autonomous Agents in a Multi-Agent World: MultiAgent System Engineering
Variable forgetting in reasoning about knowledge
Journal of Artificial Intelligence Research
Strongly complete axiomatizations of “knowing at most” in syntactic structures
CLIMA'05 Proceedings of the 6th international conference on Computational Logic in Multi-Agent Systems
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Levesque introduced a notion of "only knowing", with the goal of capturing certain types of nonmonotonic reasoning. Levesque's logic dealt with only the case of a single agent. Recently, both Halpern and Lakemeyer independently attempted to extend Levesque's logic to the multi-agent case. Although there are a number of similarities in their approaches, there are some significant differences. In this paper, we reexamine the notion of only knowing, going back to first principles. In the process, we point out some problems with the earlier definitions. This leads us to reconsider what the properties of only knowing ought to be. We provide an axiom system that captures our desiderata, and show that it has a semantics that corresponds to it. The axiom system has an added feature of interest: it includes a modal operator for satisfiability, and thus provides a complete axiomatization for satisfiability in the logic K45.