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

Abstract : 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.
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https://hal.archives-ouvertes.fr/hal-01090640
Contributor : Miguel Couceiro <>
Submitted on : Wednesday, December 3, 2014 - 8:07:42 PM
Last modification on : Tuesday, December 18, 2018 - 4:38:02 PM

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Miguel Couceiro, Lucien Haddad, Karsten Schölzel, Tamas Waldhauser. A Solution to a Problem of D. Lau: Complete Classification of Intervals in the Lattice of Partial Boolean Clones. IEEE 43rd International Symposium on Multiple-Valued Logic (ISMVL), 2013, May 2013, Toyama, Japan. ⟨10.1109/ISMVL.2013.7⟩. ⟨hal-01090640⟩

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