A formally verified abstract account of Gödel's incompleteness theorems

Popescu, Andrei and Traytel, Dmitriy (2019) A formally verified abstract account of Gödel's incompleteness theorems. Fontaine, Pascal, ed. Automated Deduction – CADE 27. CADE 2019. Lecture Notes in Computer Science, vol 11716. In: CADE 27 - 27th International Conference on Automated Deduction, 27-30 Aug 2019, Natel, Brazil. ISBN 9783030294359, e-ISBN 9783030294366. ISSN 0302-9743 (doi:10.1007/978-3-030-29436-6_26)

[img]
Preview
PDF - Final accepted version (with author's formatting)
Download (227kB) | Preview

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 S ́wierczkowski–Paulson semantics-based approach. As part of our framework’s validation, we upgrade Paulson’s Isabelle proof to produce a mech- anization 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.

Item Type: Conference or Workshop Item (Paper)
Additional Information: Popescu A., Traytel D. (2019) A Formally Verified Abstract Account of Gödel’s Incompleteness Theorems. In: Fontaine P. (eds) Automated Deduction – CADE 27. CADE 2019. Lecture Notes in Computer Science, vol 11716. Springer, Cham
Research Areas: A. > School of Science and Technology > Computer Science
Item ID: 28147
Notes on copyright: This is the Author’s accepted version of a paper published in Automated Deduction – CADE 27. CADE 2019. Lecture Notes in Computer Science, vol 11716 . The final authenticated version is available online at https://doi.org/10.1007/978-3-030-29436-6_26
Useful Links:
Depositing User: Andrei Popescu
Date Deposited: 12 Nov 2019 09:25
Last Modified: 22 Nov 2019 21:03
URI: https://eprints.mdx.ac.uk/id/eprint/28147

Actions (login required)

Edit Item Edit Item

Full text downloads (NB count will be zero if no full text documents are attached to the record)

Downloads per month over the past year