Relation Graphs and Partial Clones on a 2-Element Set

Miguel Couceiro (1, 2) , Lucien Haddad (3) , Karsten Schölzel (4) , Tamas Waldhauser (5)

1 LAMSADE - Laboratoire d'analyse et modélisation de systèmes pour l'aide à la décision
2 ORPAILLEUR - Knowledge representation, reasonning
3 RMCC - Royal Military College of Canada
4 Mathematics Research Unit
5 Bolyai Institute [Szeged]

In a recent paper, the authors show that the sublattice of partial clones that preserve the relation {(0,0),(0,1),(1,0)} is of continuum cardinality on 2. In this paper we give an alternative proof to this result by making use of a representation of relations derived from {(0,0),(0,1),(1,0)} in terms of certain types of graphs. As a by-product, this tool brings some light into the understanding of the structure of this uncountable sublattice of strong partial clones.

Domaines: Mathématiques [math]; Informatique [cs]

Miguel Couceiro, Lucien Haddad, Karsten Schölzel, Tamas Waldhauser. Relation Graphs and Partial Clones on a 2-Element Set. IEEE 44th International Symposium on Multiple-Valued Logic (ISMVL), 2014, May 2014, Bremen, Germany. pp.161-166, ⟨10.1109/ISMVL.2014.36⟩. ⟨hal-01090638⟩