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

Reference : A Solution to a Problem of D. Lau: Complete Classification of Intervals in the Lattic...


	Document type :	Scientific congresses, symposiums and conference proceedings : Paper published in a journal
	Discipline(s) :	Physical, chemical, mathematical & earth Sciences : Mathematics
	To cite this reference:	http://hdl.handle.net/10993/9232

Title :	A Solution to a Problem of D. Lau: Complete Classification of Intervals in the Lattice of Partial Boolean Clones
Language :	English
Author, co-author :	Schölzel, Karsten [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >]
	Couceiro, Miguel [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >]
	Haddad, Lucien [> >]
	Waldhauser, Tamas [> >]
Publication date :	2013
Journal title :	Multiple-Valued Logic (ISMVL), 2013 IEEE 43rd International Symposium on
Peer reviewed :	Yes
Audience :	International
ISSN :	0195-623X
Event name :	IEEE 43rd International Symposium on Multiple-Valued Logic ISMVL-2013
Event date :	from 21-05-2013 to 24-05-2013
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.
Target :	Researchers
Permalink :	http://hdl.handle.net/10993/9232
DOI :	10.1109/ISMVL.2013.7

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