, Volume 190, Supplement 1, pp 31–55 | Cite as

Information dynamics and uniform substitution

  • Wesley H. Holliday
  • Tomohiro Hoshi
  • Thomas F. IcardIII


The picture of information acquisition as the elimination of possibilities has proven fruitful in many domains, serving as a foundation for formal models in philosophy, linguistics, computer science, and economics. While the picture appears simple, its formalization in dynamic epistemic logic reveals subtleties: given a valid principle of information dynamics in the language of dynamic epistemic logic, substituting complex epistemic sentences for its atomic sentences may result in an invalid principle. In this article, we explore such failures of uniform substitution. First, we give epistemic examples inspired by Moore, Fitch, and Williamson. Second, we answer affirmatively a question posed by van Benthem: can we effectively decide when every substitution instance of a given dynamic epistemic principle is valid? In technical terms, we prove the decidability of this schematic validity problem for public announcement logic (PAL and PAL-RC) over models for finitely many fully introspective agents, as well as models for infinitely many arbitrary agents. The proof of this result illuminates the reasons for the failure of uniform substitution.


Dynamic epistemic logic Public announcement logic Uniform substitution Schematic validity Substitution core Decidability 



We wish to thank Johan van Benthem for stimulating our interest in the topic of this article and the anonymous referees for helpful comments. This article is based on our earlier conference paper (Holliday et al. 2011) presented at the 2011 LORI-III Workshop in Guangzhou, China. We are grateful to the workshop organizers and participants for valuable discussion.


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Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  • Wesley H. Holliday
    • 1
    • 2
  • Tomohiro Hoshi
    • 2
    • 3
  • Thomas F. IcardIII
    • 2
    • 4
  1. 1.Department of PhilosophyUniversity of CaliforniaBerkeleyUSA
  2. 2.Logical Dynamics LabCenter for the Study of Language and InformationStanfordUSA
  3. 3.Stanford Pre-Collegiate StudiesStanford UniversityStanfordUSA
  4. 4.Department of PhilosophyStanford UniversityStanfordUSA

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