Truth-Tracking by Belief Revision

Alexandru Baltag, Nina Gierasimczuk*, Sonja Smets

*Corresponding author for this work

Research output: Contribution to journalJournal articleResearchpeer-review

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Abstract

We study the learning power of iterated belief revision methods. Successful learning is understood as convergence to correct, i.e., true, beliefs. We focus on the issue of universality: whether or not a particular belief revision method is able to learn everything that in principle is learnable. We provide a general framework for interpreting belief revision policies as learning methods. We focus on three popular cases: conditioning, lexicographic revision, and minimal revision. Our main result is that conditioning and lexicographic revision can drive a universal learning mechanism, provided that the observations include only and all true data, and provided that a non-standard, i.e., non-well-founded prior plausibility relation is allowed. We show that a standard, i.e., well-founded belief revision setting is in general too narrow to guarantee universality of any learning method based on belief revision. We also show that minimal revision is not universal. Finally, we consider situations in which observational errors (false observations) may occur. Given a fairness condition, which says that only finitely many errors occur, and that every error is eventually corrected, we show that lexicographic revision is still universal in this setting, while the other two methods are not.

Original languageEnglish
JournalStudia Logica
Volume107
Issue number5
Pages (from-to)917-947
Number of pages31
ISSN0039-3215
DOIs
Publication statusPublished - 2019

Keywords

  • Belief revision
  • Dynamic Epistemic Logic
  • Formal learning theory
  • Truth-tracking

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