Light Dialectica revisited

doi:10.1016/j.apal.2010.04.008

Annals of Pure and Applied Logic

Volume 161, Issue 11, August 2010, Pages 1379-1389

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Abstract

We upgrade the light Dialectica interpretation (Hernest, 2005) [6] by adding two more light universal quantifiers, which are both semi-computational and semi-uniform and complement each other. An illustrative example is presented for the new light quantifiers and a new application is given for the older uniform quantifier. The realizability of new light negative formulations for the Axiom of Choice and for the Independence of Premises is explored in the new setting.

MSC

03D15

03D65

03F20

03F10

Keywords

Computational content of proofs

Functional interpretations

Program extraction from proofs

Light Dialectica interpretation

Light/uniform quantifiers

Automated program synthesis