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Interactive Realizability for second-order Heyting arithmetic with EM1 and SK1

Published online by Cambridge University Press:  25 October 2013

FEDERICO ASCHIERI
FEDERICO ASCHIERI*
Affiliation:
Laboratoire de l'Informatique du Parallélisme (UMR 5668), équipe Plume, École Normale Supérieure de Lyon – Université de Lyon, 46 Allée d'Italie, 69007 Lyon, France Email: federico.aschieri@ens-lyon.fr
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Abstract

We introduce a realizability semantics based on interactive learning for full second-order Heyting arithmetic with excluded middle and Skolem axioms over Σ10-formulas. Realizers are written in a classical version of Girard's System $\mathsf{F}$ and can be viewed as programs that learn by interacting with the environment. We show that the realizers of any Π20-formula represent terminating learning processes whose outcomes are numerical witnesses for the existential quantifier of the formula.

Type
Paper
Information
Mathematical Structures in Computer Science , Volume 24 , Issue 6 , December 2014 , e240601
Copyright
Copyright © Cambridge University Press 2013 

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