Kürbis, Nils;
(2024)
Normalisation for negative free logics without and with definite descriptions.
The Review of Symbolic Logic
pp. 1-33.
10.1017/S1755020324000157.
(In press).
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Abstract
This paper proves normalisation theorems for intuitionist and classical negative free logic, without and with the operator for definite descriptions. Rules specific to free logic give rise to new kinds of maximal formulas additional to those familiar from standard intuitionist and classical logic. When is added it must be ensured that reduction procedures involving replacements of parameters by terms do not introduce new maximal formulas of higher degree than the ones removed. The problem is solved by a rule that permits restricting these terms in the rules for ∀ , ∃ and to parameters or constants. A restricted subformula property for deductions in systems without is considered. It is improved upon by an alternative formalisation of free logic building on an idea of Jaśkowski’s. In the classical system the rules for require treatment known from normalisation for classical logic with ∨ or ∃ . The philosophical significance of the results is also indicated.
| Type: | Article |
|---|---|
| Title: | Normalisation for negative free logics without and with definite descriptions |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1017/S1755020324000157 |
| Publisher version: | http://dx.doi.org/10.1017/s1755020324000157 |
| Language: | English |
| Additional information: | Copyright © The Author(s), 2024. Published by Cambridge University Press on behalf of The Association for Symbolic Logic. This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (https://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited. |
| Keywords: | Negative free logic; definite descriptions; proof theory; normalisation |
| 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/10199855 |
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