  This study focuses on category formation for individual agents and the
dynamics of symbol emergence in a multi-agent system through semiotic
communication. Semiotic communication is defined, in this study, as the
generation and interpretation of signs associated with the categories formed
through the agent's own sensory experience or by exchange of signs with other
agents. From the viewpoint of language evolution and symbol emergence,
organization of a symbol system in a multi-agent system is considered as a
bottom-up and dynamic process, where individual agents share the meaning of
signs and categorize sensory experience. A constructive computational model can
explain the mutual dependency of the two processes and has mathematical support
that guarantees a symbol system's emergence and sharing within the multi-agent
system. In this paper, we describe a new computational model that represents
symbol emergence in a two-agent system based on a probabilistic generative
model for multimodal categorization. It models semiotic communication via a
probabilistic rejection based on the receiver's own belief. We have found that
the dynamics by which cognitively independent agents create a symbol system
through their semiotic communication can be regarded as the inference process
of a hidden variable in an interpersonal multimodal categorizer, if we define
the rejection probability based on the Metropolis-Hastings algorithm. The
validity of the proposed model and algorithm for symbol emergence is also
verified in an experiment with two agents observing daily objects in the
real-world environment. The experimental results demonstrate that our model
reproduces the phenomena of symbol emergence, which does not require a teacher
who would know a pre-existing symbol system. Instead, the multi-agent system
can form and use a symbol system without having pre-existing categories.
