Implicatively Precomplete Sets of Multioperations Defined on a Set of Three Elements

Abstract

We study the completeness criterion on the set of rank-3 multioperations with respect to the implicative closure operator. The problem is a special case of the problem of finite classification of multioperations defined on an arbitrary set. A description of all precomplete sets is obtained. The expressive possibilities of the operator are described, including the conditions under which a set of operations implicatively generates all sets of multoperations. The obtained result can be used in the study of multioperations defined on an arbitrary set.

Keywords

• closure
• multioperation
• closed set
• composition
• completeness
• representability