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A Solution to a Problem of D. Lau: Complete Classification of Intervals in the Lattice of Partial Boolean Clones

Couceiro, Miguel; Haddad, Lucien; Schölzel, Karsten; Waldhauser, Tamás (2017), A Solution to a Problem of D. Lau: Complete Classification of Intervals in the Lattice of Partial Boolean Clones, Journal of Multiple-Valued Logic and Soft Computing, 28, 1, p. 47-58

Type
Article accepté pour publication ou publié
External document link
https://hal.inria.fr/hal-01183004
Date
2017
Journal name
Journal of Multiple-Valued Logic and Soft Computing
Volume
28
Number
1
Publisher
OCP Science
Pages
47-58
Metadata
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Author(s)
Couceiro, Miguel
Laboratoire d'analyse et modélisation de systèmes pour l'aide à la décision [LAMSADE]
Haddad, Lucien
Royal Military College of Canada [RMCC]
Schölzel, Karsten
Mathematics Research Unit
Waldhauser, Tamás
Bolyai Institute [Szeged]
Abstract (EN)
The following natural problem, first considered by D. Lau, has been tackled by several authors recently: Let C be a total clone on 2 := {0, 1}. Describe the interval I(C) of all partial clones on 2 whose total component is C. We establish some results in this direction and combine them with previous ones to show the following dichotomy result: For every total clone C on 2, the set I(C) is either finite or of continuum cardinality.
Subjects / Keywords
Partial boolean clones