DagSemProc.05021.23.pdf
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Unifying Functional Interpretations
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Dagstuhl Seminar Proceedings, Volume 5021
Series: Dagstuhl Seminar Proceedings (DagSemProc) - License:
Creative Commons Attribution 4.0 International license
- Publication Date: 2006-01-16
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Paulo Oliva. Unifying Functional Interpretations. In Mathematics, Algorithms, Proofs. Dagstuhl Seminar Proceedings, Volume 5021, pp. 1-20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2006)
https://doi.org/10.4230/DagSemProc.05021.23
Abstract
The purpose of this article is to present a parametrised functional interpretation. Depending on the choice of the two parameters one obtains well-known functional interpretations, among others Gödel's Dialectica interpretation, Diller-Nahm's variant of the Dialectica interpretation, Kreisel's modified realizability, Kohlenbach's monotone interpretations and Stein's family of functional interpretations. We show that all these interpretations only differ on two basic choices, which are captured by the parameters, namely the choices of (1) "how much" of the counter-examples for A becomes witnesses for the negation of A, and of (2) "how much" information about the witnesses of A one is interested in.
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Keywords
- Functional interpretation
- modified realizability
- Dialectica interpretation
- intuitionistic logic
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