  We define a class of algebras describing links of binary semi-isolating
formulas on a set of realizations for a family of 1-types of a complete theory.
These algebras include algebras of isolating formulas considered before. We
prove that a set of labels for binary semi-isolating formulas on a set of
realizations for a 1-type forms a monoid of a special form with a partial order
inducing ranks for labels, with set-theoretic operations, and with a
composition. We describe the class of these structures. A description of the
class of structures relative to families of 1-types is given.
