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 [Conference or Workshop Item] (doi:10.1007/978-3-030-29436-6_26)

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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
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Depositing User: Andrei Popescu
Date Deposited: 12 Nov 2019 09:25
Last Modified: 11 Jun 2021 15:32
URI: https://eprints.mdx.ac.uk/id/eprint/28147

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