Title :
The Lattice of the Clones of Self-Dual Functions in Three-Valued Logic
Author_Institution :
Dept. of Math. & Mech., Moscow State Univ. Moscow, Moscow, Russia
Abstract :
The lattice of all clones of self-dual functions in three-valued logic is described in the paper. Even though this lattice contains a continuum of clones, a simple description was found. Using this description different properties of the lattice and of the clones were derived. Pair wise inclusion of the clones into each other was described, and all finitely generated clones were found. Also, for each clone the relation degree, the cardinality of the set of all clones containing this clone, and the cardinality of the set of all clones that are contained in this clone were determined.
Keywords :
multivalued logic; cardinality; clone lattice; self-dual functions; three-valued logic; Algebra; Cloning; Delta modulation; Frequency modulation; Lattices; Manganese; clone; closed class; functions; lattice; self-dual; three-valued;
Conference_Titel :
Multiple-Valued Logic (ISMVL), 2011 41st IEEE International Symposium on
Conference_Location :
Tuusula
Print_ISBN :
978-1-4577-0112-2
Electronic_ISBN :
0195-623X
DOI :
10.1109/ISMVL.2011.16
