Notre Dame Journal of Formal Logic

Periodicity of Negation

Athanassios Tzouvaras

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.

Article information

Source
Notre Dame J. Formal Logic, Volume 42, Number 2 (2001), 87-99.

Dates
First available in Project Euclid: 5 June 2003

Permanent link to this document
https://projecteuclid.org/euclid.ndjfl/1054837935

Digital Object Identifier
doi:10.1305/ndjfl/1054837935

Mathematical Reviews number (MathSciNet)
MR1993392

Zentralblatt MATH identifier
1031.03077

Subjects
Primary: 03G10: Lattices and related structures [See also 06Bxx]
Secondary: 03B99: None of the above, but in this section

Keywords
distributive lattice negation periodic function

Citation

Tzouvaras, Athanassios. Periodicity of Negation. Notre Dame J. Formal Logic 42 (2001), no. 2, 87--99. doi:10.1305/ndjfl/1054837935. https://projecteuclid.org/euclid.ndjfl/1054837935


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