Journal of Logic, Language and Information

, Volume 25, Issue 1, pp 1–35

Announcements to Attentive Agents

  • Thomas Bolander
  • Hans van Ditmarsch
  • Andreas Herzig
  • Emiliano Lorini
  • Pere Pardo
  • François Schwarzentruber
Article

DOI: 10.1007/s10849-015-9234-3

Cite this article as:
Bolander, T., van Ditmarsch, H., Herzig, A. et al. J of Log Lang and Inf (2016) 25: 1. doi:10.1007/s10849-015-9234-3

Abstract

In public announcement logic it is assumed that all agents pay attention to the announcement. Weaker observational conditions can be modelled in action model logic. In this work, we propose a version of public announcement logic wherein it is encoded in the states of the epistemic model which agents pay attention to the announcement. This logic is called attention-based announcement logic. We give an axiomatization of the logic and prove that complexity of satisfiability is the same as that of public announcement logic, and therefore lower than that of action model logic. An attention-based announcement can also be described as an action model. We extend our logic by integrating attention change. Finally, we add the notion of common belief to the language, we exploit this to formalize the concept of joint attention, that has been widely discussed in the philosophical and cognitive science literature, and we provide a corresponding axiomatization. This axiomatization also employs the auxiliary notion of attention-based relativized common belief.

Keywords

Dynamic epistemic logic Axiomatization Satisfiability  Common belief Collective attention 

Copyright information

© Springer Science+Business Media Dordrecht 2015

Authors and Affiliations

  • Thomas Bolander
    • 1
  • Hans van Ditmarsch
    • 2
  • Andreas Herzig
    • 3
  • Emiliano Lorini
    • 3
    • 4
  • Pere Pardo
    • 2
  • François Schwarzentruber
    • 5
  1. 1.DTU ComputeTechnical University of DenmarkCopenhagenDenmark
  2. 2.LORIA, CNRSUniversity of LorraineVandœuvre-lés-NancyFrance
  3. 3.CNRS, IRITUniversity of ToulouseToulouseFrance
  4. 4.IASTToulouseFrance
  5. 5.ENS RennesIRISARennesFrance