Synthese

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

Information dynamics and uniform substitution

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

Abstract

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.

Keywords

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

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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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