Algebras of distributions for isolating formulas of a complete theory

We define a class of algebras describing links of binary isolating formulas on a set of realizations for a family of $1$-types of a complete theory. We prove that a set of labels for binary isolating formulas on a set of realizations for a $1$-type $p$ forms a groupoid of a special form if there is an atomic model over a realization of $p$. We describe the class of these groupoids and consider features of these groupoids in a general case and for special theories. A description of the class of partial groupoids relative to families of $1$-types is given.