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
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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: |
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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: | https://doi.org/10.1007/978-3-030-29436-6_26 |
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