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A Dynamic Logic for Learning Theory

  • Alexandru Baltag
  • Nina Gierasimczuk
  • Aybüke Özgün
  • Ana Lucia Vargas SandovalEmail author
  • Sonja Smets
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10669)

Abstract

Building on previous work [4, 5] that bridged Formal Learning Theory and Dynamic Epistemic Logic in a topological setting, we introduce a Dynamic Logic for Learning Theory (DLLT), extending Subset Space Logics [9, 17] with dynamic observation modalities \([o]\varphi \), as well as with a learning operator Open image in new window , which encodes the learner’s conjecture after observing a finite sequence of data Open image in new window . We completely axiomatise DLLT, study its expressivity and use it to characterise various notions of knowledge, belief, and learning.

Keywords

Learning theory Dynamic epistemic logic Modal Logic Subset Space Semantics Inductive knowledge Epistemology 

Notes

Acknowledgements

The research of Nina Gierasimczuk is supported by an Innovational Research Incentives Scheme Veni grant 275-20-043, Netherlands Organisation for Scientific Research (NWO) and by the OPUS grant 2015/19/B/HS1/03292, National Science Centre Poland (NCN). Aybüke Özgün acknowledges financial support from European Research Council grant EPS 313360.

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Copyright information

© Springer International Publishing AG 2018

Authors and Affiliations

  • Alexandru Baltag
    • 1
  • Nina Gierasimczuk
    • 2
  • Aybüke Özgün
    • 1
    • 3
  • Ana Lucia Vargas Sandoval
    • 1
    Email author
  • Sonja Smets
    • 1
  1. 1.ILLCUniversity of AmsterdamAmsterdamThe Netherlands
  2. 2.DTU ComputeTechnical University of DenmarkCopenhagenDenmark
  3. 3.LORIA, CNRS-Université de LorraineNancyFrance

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