Year: 2024
Type: article
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 $\forall $ , $\exists $ 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 $\lor $ or $\exists $ . The philosophical significance of the results is also indicated.
Source: The Review of Symbolic Logic
Author: NILS KÜRBIS
Language: English
Topic: Advanced Algebra and Logic
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,450
OpenAlex ID: W4402194924