Interactive Learning Based Realizability and 1-Backtracking Games

Details Interactive Learning Based Realizability and 1-Backtracking Games Interactive Learning Based Realizability and 1-Backtracking Games

2011-01-28

arxiv.org/abs/1101.5441v1

EPTCS 47, 2011, pp. 6-20

Computer Science

Logic in Computer Science

In Proceedings CL&C 2010, arXiv:1101.5200

Scientific paper

10.4204/EPTCS.47.3

We prove that interactive learning based classical realizability (introduced by Aschieri and Berardi for first order arithmetic) is sound with respect to Coquand game semantics. In particular, any realizer of an implication-and-negation-free arithmetical formula embodies a winning recursive strategy for the 1-Backtracking version of Tarski games. We also give examples of realizer and winning strategy extraction for some classical proofs. We also sketch some ongoing work about how to extend our notion of realizability in order to obtain completeness with respect to Coquand semantics, when it is restricted to 1-Backtracking games.

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