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Definite Descriptions in Intuitionist Positive Free Logic

Kürbis, N; (2021) Definite Descriptions in Intuitionist Positive Free Logic. Logic and Logical Philosophy , 30 pp. 327-358. 10.12775/llp.2020.024. Green open access

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Abstract

This paper presents rules of inference for a binary quantifier I for the formalisation of sentences containing definite descriptions within intuitionist positive free logic. I binds one variable and forms a formula from two formulas. Ix[F,G] means ‘The F is G’. The system is shown to have desirable proof-theoretic properties: it is proved that deductions in it can be brought into normal form. The discussion is rounded up by comparisons between the approach to the formalisation of definite descriptions recommended here and the more usual approach that uses a term-forming operator ι, where ιxF means ‘the F’.

Type: Article
Title: Definite Descriptions in Intuitionist Positive Free Logic
Open access status: An open access version is available from UCL Discovery
DOI: 10.12775/llp.2020.024
Publisher version: http://dx.doi.org/10.12775/llp.2020.024
Language: English
Additional information: © 2020 by Nicolaus Copernicus University in Toruń. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/)
Keywords: Free logic; definite descriptions; proof theory; normalisation; intuitionist logic; binary quantifiers; term forming operators
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/10116391
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