Reasoning about Only Knowing with Many Agents

Joseph Y. Halpern

We extend two notions of "only knowing", that of Halpern and Moses [1984], and that of Levesque [1990], to many agents. The main lesson of this paper is that these approaches do have reasonable extensions to the multi-agent case. Our results also shed light on the single-agent case. For example, it was always viewed as significant that the HM notion of only knowing was based on S5, while Levesque’s was based on K45. In fact, our results show that the HM notion is better understood in the context of K45. Indeed, in the single-agent case, the HM notion remains unchanged if we use K45 (or KD45) instead of S5. However, in the multi-agent case, there are significant differences between K45 and S5. Moreover, all the results proved by Halpern and Moses for the single-agent case extend naturally to the multi-agent case for K45, but not for S5.

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