The Logic of Communication Graphs

  • Eric Pacuit
  • Rohit Parikh
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3476)

Abstract

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.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Eric Pacuit
    • 1
  • Rohit Parikh
    • 2
  1. 1.Computer Science DepartmentThe Graduate Center of CUNYNew York City
  2. 2.CS, Math and PhilosophyBrooklyn College and The Graduate Center of CUNYNew York City

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