Notre Dame Journal of Formal Logic

Periodicity of Negation

Athanassios Tzouvaras


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

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

First available in Project Euclid: 5 June 2003

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

distributive lattice negation periodic function


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

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