A theory of knowledge and ignorance for many agents (Q2785840)

This paper aims to extend the notion of ``only knowing'' from the single-agent case to many agents by means of appropriate modal logics. For all extensions, the basic framework is preserved: Kripke structure of possible worlds with the corresponding modalities. The only knowing with a single agent, introduced previously by J. Y. Halpern and Y. Moses, used as a possibility a common truth assignment. To extend only knowing to many agents, three notions of possibility are defined. The first one is most appropriate for non-introspective modal systems, such as \(\text{K}_n\), \(\text{T}_n\), \(\text{S}4_n\), the second one for systems like \(\text{K}45_n\) and \(\text{KD}45_n\), and the third one for \(\text{S}5_n\) logic. With the notion of possibility accepted, reasonable extensions are shown. In the last section some interesting questions about the notion of possibility are stated to be analyzed in future work.