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Communication Pattern Logic: Epistemic and Topological Views

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Abstract

We propose communication pattern logic. A communication pattern describes how processes or agents inform each other, independently of the information content. The full-information protocol in distributed computing is the special case wherein all agents inform each other. We study this protocol in distributed computing models where communication might fail: an agent is certain about the messages it receives, but it may be uncertain about the messages other agents have received. In a dynamic epistemic logic with distributed knowledge and with modalities for communication patterns, the latter are interpreted by updating Kripke models. We propose an axiomatization of communication pattern logic, and we show that collective bisimilarity (comparing models on their distributed knowledge) is preserved when updating models with communication patterns. We can also interpret communication patterns by updating simplicial complexes, a well-known topological framework for distributed computing. We show that the different semantics correspond, and propose collective bisimulation between simplicial complexes.

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Acknowledgements

We thank the reviewers for their constructive comments, and for their encouragement to substantially expand the original submission. Armando Castañeda was partially supported by PAPIIT projects IN108720 and IN108723. Hans van Ditmarsch is grateful to Sergio Rajsbaum for opening his eyes to the beautiful duality between Kripke models and simplicial complexes, during Hans’ visit to Mexico in 2019, and for introducing him to many of his collaborators and students, including the co-authors of this work.

Funding

Armando Castaneda, Hans van Ditmarsch, David Rosenblueth, and Diego Velazquez have no funding to declare.

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Authors and Affiliations

  1. Instituto de Matemáticas, Universidad Nacional Autónoma de México, UNAM, Mexico

    Armando Castañeda

  2. University of Toulouse, CNRS, IRIT, France

    Hans van Ditmarsch

  3. Instituto de Investigaciones en Matemáticas Aplicadas y en Sistemas, Universidad Nacional Autónoma de México, UNAM, Mexico

    David A. Rosenblueth

  4. Programa de Doctorado en Ciencia e Ingenierıá de la Computación, Universidad Nacional Autónoma de México, UNAM, Mexico

    Diego A. Velázquez

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  1. Armando Castañeda
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Correspondence to Hans van Ditmarsch.

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Castañeda, A., van Ditmarsch, H., Rosenblueth, D.A. et al. Communication Pattern Logic: Epistemic and Topological Views. J Philos Logic 52, 1445–1473 (2023). https://doi.org/10.1007/s10992-023-09713-8

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