The Lattice of All Clones of Self-Dual Functions in Three-Valued Logic
The lattice of all clones of self-dual functions in three-valued logic is described. Even though this lattice contains a continuum of clones, a simple description was found. Using this description various properties of the lattice and of the clones were derived. Pairwise inclusion of the clones into each other was described, and bases for all clones were found. Also, for each clone the relation degree, the cardinalities of the corresponding principal filter and principal ideal were determined.
Keywords: Lattice, clone, self-dual function, relational clone, essential predicate, essential relation, three-valued, maximal clone.