Structure of clones in the precomplete class of self-dual functions in three-valued logic

Structure of clones in the precomplete class of self-dual functions in three-valued logic is studied. Three families of clones are defined such as finite, countable, and continual, and this description is used to establish various properties of the lattice. A set of all positive integers is considered whose elements are called functions in three-valued logic. The closure operator with respect to superposition on the set is defined in the standard manner. Predicates are represented as matrices with the columns given by tuples at which the predicate takes a value of 1. Each set of predicates is associated with the set of predicates that are dual with respect to the replacement of zero by one. Conditions that define a one-to-one correspondence between the elements of the set of tuples and the elements of the set of all predicates are found.