  We consider an approach to constructing a non-anticipating selection of a
multivalued mapping; such a problem arises in control theory under conditions
of uncertainty. The approach is called "unlocking of predicate" and consists in
the reduction of finding the truth set of a predicate to searching fixed points
of some mappings. Unlocking of predicate gives an extra opportunity to analyze
the truth set and to build its elements with desired properties.
  In this article, we outline how to build "unlocking mappings" for some
general types of predicates: we give a formal definition of the predicate
unlocking operation, the rules for the construction and calculation of
"unlocking mappings" and their basic properties. As an illustration, we
routinely construct two unlocking mappings for the predicate "be
non-anticipating mapping" and then on this base we provide the expression for
the greatest non-anticipating selection of a given multifunction.
