Resolving Distributed Knowledge

Thomas Ågotnes
(University of Bergen)
Yì N. Wáng
(Zhejiang University)

Distributed knowledge is the sum of the knowledge in a group; what someone who is able to discern between two possible worlds whenever any member of the group can discern between them, would know. Sometimes distributed knowledge is referred to as the potential knowledge of a group, or the joint knowledge they could obtain if they had unlimited means of communication. In epistemic logic, the formula D_Gφ is intended to express the fact that group G has distributed knowledge of φ, that there is enough information in the group to infer φ. But this is not the same as reasoning about what happens if the members of the group share their information. In this paper we introduce an operator R_G, such that R_Gφ means that φ is true after G have shared all their information with each other – after G's distributed knowledge has been resolved. The R_G operators are called resolution operators. Semantically, we say that an expression R_Gφ is true iff φ is true in what van Benthem [11, p. 249] calls (G's) communication core; the model update obtained by removing links to states for members of G that are not linked by all members of G. We study logics with different combinations of resolution operators and operators for common and distributed knowledge. Of particular interest is the relationship between distributed and common knowledge. The main results are sound and complete axiomatizations.

In R Ramanujam: Proceedings Fifteenth Conference on Theoretical Aspects of Rationality and Knowledge (TARK 2015), Carnegie Mellon University, Pittsburgh, USA, June 4-6, 2015, Electronic Proceedings in Theoretical Computer Science 215, pp. 31–50.
Published: 23rd June 2016.

ArXived at: http://dx.doi.org/10.4204/EPTCS.215.4 bibtex PDF
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