On variable non-dependence of first-order formulas

Fuente: arXiv

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Bibliographische Detailangaben
Hauptverfasser:	Lefever, Koen, Székely, Gergely
Format:	Preprint
Veröffentlicht:	2025
Schlagworte:	Logic
Online-Zugang:	Acceder al recurso
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author	Lefever, Koen Székely, Gergely
author_facet	Lefever, Koen Székely, Gergely
contents	In this paper, we introduce a concept of non-dependence of variables in formulas. A formula in first-order logic is non-dependent of a variable if the truth value of this formula does not depend on the value of that variable. This variable non-dependence can be subject to constraints on the value of some variables which appear in the formula, these constraints are expressed by another first-order formula. After investigating its basic properties, we apply this concept to simplify convoluted formulas by bringing out and discarding redundant nested quantifiers. Such convoluted formulas typically appear when one uses a translation function interpreting a theory into another.
format	Preprint
id	arxiv_https___arxiv_org_abs_2501_16633
institution	arXiv
publishDate	2025
record_format	arxiv
spellingShingle	On variable non-dependence of first-order formulas Lefever, Koen Székely, Gergely Logic In this paper, we introduce a concept of non-dependence of variables in formulas. A formula in first-order logic is non-dependent of a variable if the truth value of this formula does not depend on the value of that variable. This variable non-dependence can be subject to constraints on the value of some variables which appear in the formula, these constraints are expressed by another first-order formula. After investigating its basic properties, we apply this concept to simplify convoluted formulas by bringing out and discarding redundant nested quantifiers. Such convoluted formulas typically appear when one uses a translation function interpreting a theory into another.
title	On variable non-dependence of first-order formulas
topic	Logic
url	https://arxiv.org/abs/2501.16633

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