2026-07-22T21:02:15Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:25443 2026-03-19T13:28:37Z ddc:004 open_access

A Unifying Conservation Theorem Fellin, Giulio double negation negative translation conservation minimal logic Glivenko’s theorem The relationship between classical and constructive logics has long been illuminated by a series of conservation results, beginning with Kolmogorov’s negative translation and Glivenko’s double negation theorem, and later extended by Kuroda and Segerberg to first-order and minimal logics respectively. These results reveal how certain classical principles can be interpreted or recovered within weaker constructive frameworks, either via translations or through minimal extensions that satisfy specific logical properties. In this paper, we propose a unifying generalisation of these conservation theorems, that consolidates and expands the abstract methods introduced in earlier studies, offering a unified perspective on the interplay between classical provability and constructive reasoning. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Giulio Fellin 2026 Is Part Of LIPIcs, Volume 363, 34th EACSL Annual Conference on Computer Science Logic (CSL 2026) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.CSL.2026.19 urn:nbn:de:0030-drops-254431 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2026.19 eng https://creativecommons.org/licenses/by/4.0/legalcode