Collective belief revision in linear algebra

摘要

Although the logic of belief update has mainly concerned a belief state of one agent thus far, the real world settings require us to implement simultaneous belief changes. Here, however, we need to manage so many indices: agent names, time stamps, and the difference of information. In this paper, we introduce the notation of vectors and matrices for the simultaneous informing action. By this, we show that a matrix can represent a public announcement and/or a consecutive message passing, with the time of the change of belief states properly. A collective belief state multiplied by a communication matrix, including matrices of accessibility in Kripke semantics, becomes a hypercuboid.