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2001 Periodicity of Negation
Athanassios Tzouvaras
Notre Dame J. Formal Logic 42(2): 87-99 (2001). DOI: 10.1305/ndjfl/1054837935

Abstract

In the context of a distributive lattice we specify the sort of mappings that could be generally called ''negations'' and study their behavior under iteration. We show that there are periodic and nonperiodic ones. Natural periodic negations exist with periods 2, 3, and 4 and pace 2, as well as natural nonperiodic ones, arising from the interaction of interior and quasi interior mappings with the pseudocomplement. For any n and any even $s<n$, negations of period n and pace s can also be constructed, but in a rather ad hoc and trivial way.

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Athanassios Tzouvaras. "Periodicity of Negation." Notre Dame J. Formal Logic 42 (2) 87 - 99, 2001. https://doi.org/10.1305/ndjfl/1054837935

Information

Published: 2001
First available in Project Euclid: 5 June 2003

MathSciNet: MR1993392
zbMATH: 1031.03077
Digital Object Identifier: 10.1305/ndjfl/1054837935

Subjects:
Primary: 03G10
Secondary: 03B99

Keywords: Distributive lattice , negation , periodic function

Rights: Copyright © 2001 University of Notre Dame

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Vol.42 • No. 2 • 2001
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