On the membership of multifunctions of rank two in ES I-precomplete sets

Multifunctions on a two-element set are considered together with operators of superposition and branching by an equality predicate. In superposition, a special role is assigned to the empty set, which is interpreted as "breakage". In the absence of "breakage", common elements are selected with all possible refinements. The set of common elements is declared as a superposition value. If there are no common elements, then the value of the multifunction is declared to be the set of all elements that occur with all possible refinements. For the introduced superposition and the branching operator by the equality predicate all precomplete sets are described, a completeness criterion is formulated and proved. Multifunctional classification is performed concerning belonging to precomplete sets. Examples of multifunctional classes are given. Precomplete sets are described in the language of predicate preservation by function. When performing the classification of multifunctional functions, a computer search was used.