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Normalisation and subformula property for a system of classical logic with Tarski's rule

Kurbis, N; (2021) Normalisation and subformula property for a system of classical logic with Tarski's rule. Archive for Mathematical Logic 10.1007/s00153-021-00775-6. (In press). Green open access

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Abstract

This paper considers a formalisation of classical logic using general introduction rules and general elimination rules. It proposes a definition of ‘maximal formula’, ‘segment’ and ‘maximal segment’ suitable to the system, and gives reduction procedures for them. It is then shown that deductions in the system convert into normal form, i.e. deductions that contain neither maximal formulas nor maximal segments, and that deductions in normal form satisfy the subformula property. Tarski’s Rule is treated as a general introduction rule for implication. The general introduction rule for negation has a similar form. Maximal formulas with implication or negation as main operator require reduction procedures of a more intricate kind not present in normalisation for intuitionist logic.

Type: Article
Title: Normalisation and subformula property for a system of classical logic with Tarski's rule
Open access status: An open access version is available from UCL Discovery
DOI: 10.1007/s00153-021-00775-6
Publisher version: https://doi.org/10.1007/s00153-021-00775-6
Language: English
Additional information: © 2021 Springer Nature Switzerland AG. This article is licensed under a Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/).
Keywords: Proof theory, Classical logic, Normalisation, Subformula property
UCL classification: UCL
UCL > Provost and Vice Provost Offices > UCL SLASH
UCL > Provost and Vice Provost Offices > UCL SLASH > Faculty of Arts and Humanities
UCL > Provost and Vice Provost Offices > UCL SLASH > Faculty of Arts and Humanities > Dept of Philosophy
URI: https://discovery.ucl.ac.uk/id/eprint/10128913
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