Popescu, A. orcid.org/0000-0001-8747-0619 and Traytel, D. (2019) A formally verified abstract account of Gödel’s incompleteness theorems. In: Fontaine, P., (ed.) Automated Deduction – CADE 27: 27th International Conference on Automated Deduction, Natal, Brazil, August 27–30, 2019, Proceedings. 27th International Conference on Automated Deduction, 27-30 Aug 2019, Natal, Brazil. Lecture Notes in Computer Science, LNAI 11716 . Springer International Publishing , pp. 442-461. ISBN 9783030294359
Abstract
We present an abstract development of Gödel’s incompleteness theorems, performed with the help of the Isabelle/HOL theorem prover. We analyze sufficient conditions for the theorems’ applicability to a partially specified logic. In addition to the usual benefits of generality, our abstract perspective enables a comparison between alternative approaches from the literature. These include Rosser’s variation of the first theorem, Jeroslow’s variation of the second theorem, and the Świerczkowski–Paulson semantics-based approach. As part of our framework’s validation, we upgrade Paulson’s Isabelle proof to produce a mechanization of the second theorem that does not assume soundness in the standard model, and in fact does not rely on any notion of model or semantic interpretation.
Metadata
Item Type: | Proceedings Paper |
---|---|
Authors/Creators: |
|
Editors: |
|
Copyright, Publisher and Additional Information: | © 2019 Springer Nature Switzerland AG. This is an author-produced version of a paper subsequently published in Lecture Notes in Computer Science. Uploaded in accordance with the publisher's self-archiving policy. |
Dates: |
|
Institution: | The University of Sheffield |
Academic Units: | The University of Sheffield > Faculty of Engineering (Sheffield) > Department of Computer Science (Sheffield) |
Depositing User: | Symplectic Sheffield |
Date Deposited: | 14 Oct 2022 09:39 |
Last Modified: | 15 Oct 2022 01:17 |
Status: | Published |
Publisher: | Springer International Publishing |
Series Name: | Lecture Notes in Computer Science |
Refereed: | Yes |
Identification Number: | 10.1007/978-3-030-29436-6_26 |
Related URLs: | |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:191502 |