On the Enumeration Closure Operator in Multivalued Logic

摘要

The operator of closure with respect to enumeration (the Π-operator) is defined in multivalued logic. The finiteness of the number of Π-closed classes in k-valued logic is proved. All six Π-closed classes of Boolean functions are specified. Sufficient conditions for presenting Π-closed classes in the form of classes of functions that retain certain relations are determined. The Π-closed classes are compared to positively closed classes. All Π-closed classes of homogeneous functions are described.