A-classification of idempotent functions of many-valued logic Original Research Article

A-closure on the set of functions of many-valued logic is defined as the closure under the operations of superposition and of taking the dual function with respect to a permutation in the alternating group. A-classification of functions of many-valued logic is defined with the use of the A-closure operator. The class Ik of idempotent functions is one of two (for k⩾5) and one of four (for k=4) A-precomplete classes in Pk. Twelve types of standard relations, which are called main, are defined on the set Ek. It is proved that each A-closed class of functions from Ik can be defined by a suitable choice of the main relations.