An incomplete system of modal logic
type: Item
instance of: scholarly article
title: An incomplete system of modal logic
zbMATH Open document ID: 0589.03005
DOI: 10.1007/BF00649480
author: George Boolos
author: Giovanni Sambin
published in: Journal of Philosophical Logic
publication date: 1985-01-01T00:00:00Z
review text: The authors present a new system of modal propositional logic, called GH, that is ''incomplete in the following sense: there is a sentence that is not a theorem of GH even though it is valid in every frame in which all theorems of GH are valid''. This result is discussed with regard to the interpretation of '\(\square '\) as provability. The characteristic axiom of GH may then be read as saying that the sentences which are provably ''equivalent to their own provability are in fact provable''. It is thus a formalized answer to \textit{L. Henkin}'s question in ''A problem concerning provability'' [J. Symb. Logic 17, 160 (1952)], and it is closely related to Löb's theorem.
Mathematics Subject Classification ID: 03B45
zbMATH DE Number: 3946091
zbMATH Keywords: incompleteness
zbMATH Keywords: modal propositional logic
zbMATH Keywords: provability
zbMATH Keywords: Löb's theorem
reviewed by: Wolfgang Lenzen
MaRDI profile type: Publication
cites work: Q3947664
cites work: Intensional logics without iterative axioms
full work available at URL: https://doi.org/10.1007/bf00649480
OpenAlex ID: W1985302977
description: scientific article; zbMATH DE number 3946091