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Normalisation and subformula property for a system of intuitionistic logic with general introduction and elimination rules

Kurbis, N; (2021) Normalisation and subformula property for a system of intuitionistic logic with general introduction and elimination rules. Synthese 10.1007/s11229-021-03418-8. (In press). Green open access

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Abstract

This paper studies a formalisation of intuitionistic logic by Negri and von Plato which has general introduction and elimination rules. The philosophical importance of the system is expounded. Definitions of ‘maximal formula’, ‘segment’ and ‘maximal segment’ suitable to the system are formulated and corresponding reduction procedures for maximal formulas and permutative reduction procedures for maximal segments given. Alternatives to the main method used are also considered. It is shown that deductions in the system convert into normal form and that deductions in normal form have the subformula property.

Type: Article
Title: Normalisation and subformula property for a system of intuitionistic logic with general introduction and elimination rules
Open access status: An open access version is available from UCL Discovery
DOI: 10.1007/s11229-021-03418-8
Publisher version: https://doi.org/10.1007/s11229-021-03418-8
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: Intuitionistic logic, Proof theory, Normalisation, General elimination rules, General introduction rules, Harmony, Stability
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/10137258
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