Gödel's functional interpretation and the concept of learning

Research output: Chapter in Book/Report/Conference proceedingConference contribution

1 Citation (Scopus)

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.
Original languageEnglish
Title of host publicationLICS ’16: Proceedings of the 31st Annual ACM/IEEE Symposium on Logic in Computer Science
PublisherAssociation for Computing Machinery
Pages136-145
ISBN (Print)9781450343916
DOIs
Publication statusPublished - 2016
Eventthe 31st Annual ACM/IEEE Symposium - New York, NY, USA
Duration: 5 Jul 20168 Jul 2016

Conference

Conferencethe 31st Annual ACM/IEEE Symposium
Period5/07/168/07/16

Fingerprint Dive into the research topics of 'Gödel's functional interpretation and the concept of learning'. Together they form a unique fingerprint.

Cite this