Human beings often estimate others ’ beliefs and intentions when they interact with others. Estimation of others ’ beliefs will be useful also in controlling the behavior and utterances of artificial agents, especially when lines of communication are unstable or slow. But, devising such estimation algorithms and background theories for the algorithms is difficult, because of many factors affecting one’s belief. We have proposed an algorithm that estimates others ’ beliefs from observation in the changing world. Experimental results show that this algorithm returns natural answers to various queries. However, the algorithm is only heuristic, and how the algorithm deals with beliefs and their changes is not entirely clear. We propose certain semantics based on a nonstandard structure for modal logic. By using these semantics, we shed light on a logical meaning of the belief estimation that the algorithm deals with. We also discuss how the semantics and the algorithm can be generalized
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