Basic relations for the $S$-classification of functions of multivalued logic

For sets of functions of multi-valued logic the $S$-closure is defined as the closure with respect to the operations of superposition and transition to the dual functions. To describe the $S$-closed classes lying in the $S$-precomplete class of idempotent functions we introduce some standard relations which are called basic. We prove that any \linebreak[3] $S$-closed class of idempotent functions specified by arbitrary two-place relations can be defined by appropriate basic relations as well.
The work was partially supported by the Russian Foundation for Basic Research, Grants 93–011–1525 and 95–01–01625–a.