TY  - INPR
EP  - 33
SP  - 1
AV  - public
Y1  - 2024/09/03/
TI  - Normalisation for negative free logics without and with definite descriptions
N1  - 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.
SN  - 1755-0203
UR  - http://dx.doi.org/10.1017/s1755020324000157
PB  - CAMBRIDGE UNIV PRESS
ID  - discovery10199855
N2  - 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 Ja?kowski?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.
KW  - Negative free logic; definite descriptions; 
proof theory; 
normalisation
A1  - Kürbis, Nils
JF  - The Review of Symbolic Logic
ER  -