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Inductive Inference and Reverse Mathematics

Authors Rupert Hölzl, Sanjay Jain, Frank Stephan

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Rupert Hölzl
Sanjay Jain
Frank Stephan

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Rupert Hölzl, Sanjay Jain, and Frank Stephan. Inductive Inference and Reverse Mathematics. In 32nd International Symposium on Theoretical Aspects of Computer Science (STACS 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 30, pp. 420-433, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015) https://doi.org/10.4230/LIPIcs.STACS.2015.420

Abstract

The present work investigates inductive inference from the perspective 
of reverse mathematics. Reverse mathematics is a framework which relates
the proof strength of theorems and axioms throughout many areas of
mathematics in an interdisciplinary way. The present work looks at
basic notions of learnability including Angluin's tell-tale condition and its variants for learning in the limit and for conservative learning. Furthermore, the more general criterion of partial learning is investigated. These notions are studied in the reverse mathematics context for uniformly and weakly represented families of languages. The results are stated in terms of axioms referring to domination and induction strength.

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Keywords
  • reverse mathematics
  • recursion theory
  • inductive inference
  • learning from positive data

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