On the nonexistence of minimal strong partial clones

Miguel Couceiro 1 Lucien Haddad 2 Karsten Schölzel 3
1 ORPAILLEUR - Knowledge representation, reasonning
Inria Nancy - Grand Est, LORIA - NLPKD - Department of Natural Language Processing & Knowledge Discovery
Abstract : Let k be a k-element set. We show that the lattice of all strong partial clones on k has no minimal elements. Moreover, we show that if C is a strong partial clone, then the family of all partial subclones of C is of continuum cardinality. We also show that in almost all cases, every strong partial clone contains a family of continuum cardinality of strong partial subclones.
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Miguel Couceiro, Lucien Haddad, Karsten Schölzel. On the nonexistence of minimal strong partial clones. ISMVL 2017 - 47th IEEE International Symposium on Multiple-Valued Logic, May 2017, Novi Sad, Serbia. pp.6. ⟨hal-01504011⟩

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