A General Glivenko-G\'odel Theorem for Nuclei

Autor:	Fellin, Giulio, Schuster, Peter
Rok vydání:	2021
Předmět:	Computer Science - Logic in Computer Science F.4.1
Zdroj:	EPTCS 351, 2021, pp. 51-66
Druh dokumentu:	Working Paper
DOI:	10.4204/EPTCS.351.4
Popis:	Glivenko's theorem says that, in propositional logic, classical provability of a formula entails intuitionistic provability of double negation of that formula. We generalise Glivenko's theorem from double negation to an arbitrary nucleus, from provability in a calculus to an inductively generated abstract consequence relation, and from propositional logic to any set of objects whatsoever. The resulting conservation theorem comes with precise criteria for its validity, which allow us to instantly include G\"odel's counterpart for first-order predicate logic of Glivenko's theorem. The open nucleus gives us a form of the deduction theorem for positive logic, and the closed nucleus prompts a variant of the reduction from intuitionistic to minimal logic going back to Johansson. Comment: In Proceedings MFPS 2021, arXiv:2112.13746
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2112.14049 Zobrazit plný text záznamu View this record from Arxiv