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Journal of Logic and Computation 2001 11(1):41-70; doi:10.1093/logcom/11.1.41
© 2001 by Oxford University Press
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Multi-agent Only Knowing

Joseph Y. Halpern1 and Gerhard Lakemeyer2

1 Department of Computer Science, Cornell University, Ithaca, NY 14850, USA. E-mail: halpern{at}cs.cornell.eduhttp://www.cs.cornell.edu/home/halpern 2 Department of Computer Science, Aachen University of Technology, D-52056 Aachen, GermanyE-mail: gerhard{at}cs.rwth-aachen.dehttp://www-i5.informatik.rwth-aachen.de/gerhard

Levesque introduced a notion of ‘only knowing’, with the goal of capturing certain types of non-monotonic 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 re-examine the notion of only knowing, going back to first principles. In the process, we simplify Levesque's completeness proof, and 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.

Keywords: Belief; only knowing; nonmonotonic reasoning; multi-agent systems; KD45

Accepted 23 July 1996.


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