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On variable non-dependence of first-order formulas

Lefever, Koen and Székely, Gergely (2025) On variable non-dependence of first-order formulas. [Preprint]

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Abstract

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.


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Item Type: Preprint
Creators:
CreatorsEmailORCID
Lefever, Koenkoen.lefever@vub.be0000-0001-7836-4734
Székely, Gergelyszekely.gergely@renyi.hu0000-0002-5227-069X
Keywords: First-Order Logic, Algebraic Logic, Model Theory, Cylindric Algebras, Simplification Rules, Translation Functions, Logical Interpretation, Nested Quantifiers
Subjects: Specific Sciences > Mathematics > Logic
Depositing User: Dr. Koen Lefever
Date Deposited: 28 Jan 2025 19:35
Last Modified: 28 Jan 2025 19:35
Item ID: 24630
Subjects: Specific Sciences > Mathematics > Logic
Date: 27 January 2025
URI: https://philsci-archive.pitt.edu/id/eprint/24630

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