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Announcement as effort on topological spaces.

Hans van Ditmarsch1, Sophia Knight2, Aybüke Özgün1,3

  • 11LORIA, CNRS, Université de Lorraine, Nancy, France.

Synthese
|July 16, 2019
PubMed
Summary

This study introduces a new multi-agent logic for knowledge and announcements using topological spaces. It provides complete axiomatizations for systems with S5 and S4 knowledge modalities, advancing epistemic logic research.

Keywords:
Arbitrary (public)announcementsDynamic epistemic logicSubset space logicTopology

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Area of Science:

  • Epistemic Logic
  • Topological Semantics
  • Multi-Agent Systems

Background:

  • Existing epistemic logics struggle to model arbitrary announcements.
  • Subset space semantics offer a framework for modeling knowledge and announcements.
  • Topological spaces provide a rich structure for semantic interpretation.

Purpose of the Study:

  • To propose a novel multi-agent logic incorporating public and arbitrary announcements.
  • To interpret this logic using topological spaces and subset space semantics.
  • To develop and prove completeness for axiomatizations of these logics.

Main Methods:

  • Utilizing subset space semantics on topological spaces.
  • Defining novel arbitrary announcement modalities.
  • Developing and axiomatizing logics with S5 and S4 knowledge modalities.

Main Results:

  • A complete axiomatization for a multi-agent logic with S5 knowledge and arbitrary announcements.
  • Soundness and completeness results for systems with S4 knowledge modalities.
  • Demonstrated semantic and intuitive differences for the arbitrary announcement modality.

Conclusions:

  • The proposed framework successfully integrates arbitrary announcements into epistemic logic.
  • The axiomatizations provide a formal system for reasoning about knowledge and announcements.
  • This work extends the application of topological spaces in epistemic logic.