On a linear framework for belief dynamics in multi-agent environments

Authors:
Akira Fusaoka;Katsunori Nakamura;Mitsunari Sato
Affiliations:
Department of Human and Machine Intelligence, Ritsumeikan University, Kusatsu-city, Shiga, Japan;Department of Human and Machine Intelligence, Ritsumeikan University, Kusatsu-city, Shiga, Japan;Department of Human and Machine Intelligence, Ritsumeikan University, Kusatsu-city, Shiga, Japan
Venue:
CLIMA VII'06 Proceedings of the 7th international conference on Computational logic in multi-agent systems
Year:
2006

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Abstract

In this paper, we discuss the dynamics of multi-agent belief change in the framework of linear algebra. We regard an epistemic state of each agent as an element in the vector space spanned by the basis of possible worlds, so that belief change corresponds to a linear transformation on this vector space. The compound belief states of multi-agents are treated by using the product tensor of the vector for each agent. In this formulation, the reasoning in the process of belief change can be reduced to the matrix and tensor calculation.