, Volume 169, Issue 2, pp 371–384 | Cite as

Bridging learning theory and dynamic epistemic logic

Open Access


This paper discusses the possibility of modelling inductive inference (Gold 1967) in dynamic epistemic logic (see e.g. van Ditmarsch et al. 2007). The general purpose is to propose a semantic basis for designing a modal logic for learning in the limit. First, we analyze a variety of epistemological notions involved in identification in the limit and match it with traditional epistemic and doxastic logic approaches. Then, we provide a comparison of learning by erasing (Lange et al. 1996) and iterated epistemic update (Baltag and Moss 2004) as analyzed in dynamic epistemic logic. We show that finite identification can be modelled in dynamic epistemic logic, and that the elimination process of learning by erasing can be seen as iterated belief-revision modelled in dynamic doxastic logic. Finally, we propose viewing hypothesis spaces as temporal frames and discuss possible advantages of that perspective.


Identification in the limit Learning by erasing Induction Learning by elimination Co-learning Finite identifiability Dynamic epistemic logic Dynamic doxastic logic Epistemic update Belief revision 


Open Access

This article is distributed under the terms of the Creative Commons Attribution Noncommercial License which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.


  1. Alchourrón C.E., Gärdenfors P., Makinson D. (1985) On the logic of theory change: Partial meet contraction and revision functions. The Journal of Symbolic Logic 50(2): 510–530CrossRefGoogle Scholar
  2. Angluin D. (1980) Inductive inference of formal languages from positive data. Information and Control 45(2): 117–135CrossRefGoogle Scholar
  3. Baltag A., Moss L. (2004) Logics for epistemic programs. Synthese 139(2): 165–224CrossRefGoogle Scholar
  4. Batlag, A., Moss, L. S., & Solecki, S. (1998). The logic of public announcements and common knowledge and private suspicions. In Proceedings of the 7th TARK (pp. 43–56).Google Scholar
  5. Costa Florêntio, C. (2002). Learning generalized quantifiers. In Proceedings of the 7th ESSLLI Student Session.Google Scholar
  6. Dégremont, C., & Gierasimczuk, N. (2009). Can doxastic agents learn? On the temporal structure of learning. ILLC Prepublication (PP) Series PP-2009-14, Amsterdam.Google Scholar
  7. Freivalds, R., & Zeugmann, T. (1995). Co-learning of recursive languages from positive data, RIFIS. Technical report, RIFIS-TR-CS-110, RIFIS, Kyushu University 33.Google Scholar
  8. Gierasimczuk, N. (2007). The problem of learning the semantics of quantifiers. In Proceedings of the 6th TbiLLC, Vol. 4363 of LNAI (pp. 117–126). Springer.Google Scholar
  9. Gierasimczuk, N. (2009). Identification through inductive verification. In Proceedings of the 7th TbiLLC, Vol. 5422 of LNAI (pp. 193–205). Springer.Google Scholar
  10. Gierasimczuk, N., Kurzen, L., & Velázquez-Quesada, F. (2009). Learning as interaction (manuscript).Google Scholar
  11. Gold E. (1967) Language identification in the limit. Information and Control 10: 447–474CrossRefGoogle Scholar
  12. Hintikka J. (1962) Knowledge and belief. An introduction to the logic of the two notions. Cornell University Press, IthacaGoogle Scholar
  13. Jain S., Osherson D., Royer J.S., Sharma A. (1999) Systems that learn. MIT Press, ChicagoGoogle Scholar
  14. Kelly K. (1996) The logic of reliable inquiry. Oxford University Press, OxfordGoogle Scholar
  15. Lange, S., Wiehagen, R., & Zeugmann, T. (1996). Learning by erasing. In Proceedings of the 7th international workshop on algorithmic learning theory (pp. 228–241). Springer-Verlag.Google Scholar
  16. Martin E., Osherson D. (1998) Elements of scientific inquiry. MIT Press, CambridgeGoogle Scholar
  17. Osherson D., de Jongh D., Martin E., Weinstein S. (1997) Formal learning theory. In: van Benthem J., Ter Meulen A. (eds) Handbook of logic and language. North Holland, AmsterdamGoogle Scholar
  18. Tiede H.-J. (1999) Identifiability in the limit of context-free generalized quantifiers. Journal of Language and Computation 1: 93–102Google Scholar
  19. van Benthem J. (1986) Essays in logical semantics. D. Reidel, DordrechtGoogle Scholar
  20. van Benthem, J., Gerbrandy, J., & Pacuit, E. (2007). Merging frameworks for interaction: DEL and ETL. In Proceedings of the 11th TARK (pp. 72–81).Google Scholar
  21. van Ditmarsch, H., van der Hoek, W., & Kooi, B. (2007). Dynamic epistemic logic. Springer Netherlands.Google Scholar

Copyright information

© The Author(s) 2009

Authors and Affiliations

  1. 1.Institute for Logic, Language and ComputationUniversiteit van AmsterdamAmsterdamThe Netherlands

Personalised recommendations