A-closed classes of idempotent functions of many-valued logic definable by binary relations Original Research Article

A-closure on a set of functions of many-valued logic is defined as the closure with respect to the operations of superposition and transition to dual functions with respect to permutations of the alternating group. The class Ik of idempotent functions for k⩾5 is one of two, and for k=4 is one of four A-precomplete classes in Pk. We define 12 types of standard relations over the set Ek which are called basic. We prove that any A-closed class of functions in Ik which is defined by arbitrary binary relations can be also specified by means of a suitable set of basic relations.