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Gödel’s Functional Interpretation and the Concept of Learning

Thomas Powell

Proceedings of the 31st Annual ACM/IEEE Symposium on Logic in Computer Science (LICS 2016), pp. 136 – 145, 2016..

Abstract

In this article we study Gödel’s functional interpretation from the perspective of learning. We define the notion of a learning algorithm, and show that intuitive realizers of the functional interpretation of both induction and various comprehension schemas can be given in terms of these algorithms. In the case of arithmetical comprehension, we clarify how our learning realizers compare to those obtained traditionally using bar recursion, demonstrating that bar recursive interpretations of comprehension correspond to ‘forgetful’ learning algorithms. The main purpose of this work is to gain a deeper insight into the semantics of programs extracted using the functional interpretation. However, in doing so we also aim to better understand how it relates to other interpretations of classical logic for which the notion of learning is inbuilt, such as Hilbert’s epsilon calculus or the more recent learning-based realizability interpretations of Aschieri and Berardi.

 

  PDF |    doi:10.1145/2933575.2933605  

BibTeX 

@inproceedings{TP-LICS2016,
author = "Thomas Powell",
title = "G{\"o}del's Functional Interpretation and the Concept of Learning",
booktitle = "Proceedings of the 31st Annual ACM/IEEE Symposium on Logic in
Computer Science (LICS 2016)",
pages = "136-145",
year = 2016,
doi = "10.1145/2933575.2933605"
}
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