In 1992, Moss and Parikh studied a bimodal logic of knowledge and effort called Topologic. In this current paper, Topologic is extended to the case of many agents who are assumed to have some private information at the outset, but may refine their information by acquiring information possessed by other agents, possibly via yet other agents. Let us assume that the agents are connected by a communication graph. In the communication graph, an edge from agent i to agent j means that agent i can directly receive information from agent j. Agent i can then refine its own information by learning information that j has, including information acquired by j from another agent, k. We introduce a multi-agent modal logic with knowledge modalities and a modality representing communication among agents. We show that the validities of Topologic remain valid and that the communication graph is completely determined by the validities of the resulting logic. Applications of our logic to current political dilemmas are obvious. 1

This paper deals with subset spaces where points are structured as pairs of states. Our aim is to approach a formal model of uniform topological reasoning in this way. That is, in case a uniformity underlies the topological space under consideration, the re ned reasoning model is to be sensitive to that. We show completeness and decidability of the basic modal logic arising from this setting, and discuss both possible extensions of the system and limitations