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 learningbased realizability interpretations of Aschieri and Berardi.
Original language  English 

Title of host publication  LICS ’16: Proceedings of the 31st Annual ACM/IEEE Symposium on Logic in Computer Science 
Publisher  Association for Computing Machinery 
Pages  136145 
ISBN (Print)  9781450343916 
DOIs  
Publication status  Published  2016 
Event  the 31st Annual ACM/IEEE Symposium  New York, NY, USA Duration: 5 Jul 2016 → 8 Jul 2016 
Conference
Conference  the 31st Annual ACM/IEEE Symposium 

Period  5/07/16 → 8/07/16 
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Thomas Powell
Person: Research & Teaching