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Reasoning About Distributed Knowledge of Groups with Infinitely Many Agents

Authors Michell Guzmán, Sophia Knight, Santiago Quintero, Sergio Ramírez, Camilo Rueda, Frank Valencia

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ACM Subject Classification
  • Theory of computation → Concurrency
  • Theory of computation → Distributed computing models
  • Theory of computation → Semantics and reasoning
Keywords
  • Reasoning about Groups
  • Distributed Knowledge
  • Infinitely Many Agents
  • Reasoning about Space
  • Algebraic Modeling

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Abstract

Spatial constraint systems (scs) are semantic structures for reasoning about spatial and epistemic information in concurrent systems. We develop the theory of scs to reason about the distributed information of potentially infinite groups. We characterize the notion of distributed information of a group of agents as the infimum of the set of join-preserving functions that represent the spaces of the agents in the group. We provide an alternative characterization of this notion as the greatest family of join-preserving functions that satisfy certain basic properties. We show compositionality results for these characterizations and conditions under which information that can be obtained by an infinite group can also be obtained by a finite group. Finally, we provide algorithms that compute the distributive group information of finite groups.

Cite As Get BibTex

Michell Guzmán, Sophia Knight, Santiago Quintero, Sergio Ramírez, Camilo Rueda, and Frank Valencia. Reasoning About Distributed Knowledge of Groups with Infinitely Many Agents. In 30th International Conference on Concurrency Theory (CONCUR 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 140, pp. 29:1-29:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019) https://doi.org/10.4230/LIPIcs.CONCUR.2019.29

Author Details

Michell Guzmán
  • University of Milano-Bicocca, Italy
Sophia Knight
  • University of Minnesota Duluth, MN, USA
Santiago Quintero
  • LIX École Polytechnique de Paris, France
Sergio Ramírez
  • Pontificia Universidad Javeriana de Cali, Colombia
Camilo Rueda
  • Pontificia Universidad Javeriana de Cali, Colombia
Frank Valencia
  • CNRS, LIX École Polytechnique de Paris, France
  • Pontificia Universidad Javeriana de Cali, Colombia

Funding

This work have been partially supported by the ECOS-NORD project FACTS (C19M03) and the Colciencias project CLASSIC (125171250031).

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