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

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 I-k. of idempotent functions for k greater than or equal to 5 is one of two, and for k = 4 is one of four A-precomplete classes in P-k. We define 12 types of standard relations over the set E-k. 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. (C) 2001 Elsevier Science B.V. All rights reserved.