The problems formulated for a class of expert systems with knowledge representation in the form of facts can be solved applying the logic-algebraic (LA) method. Parallel processing of logic-algebraic algorithms addresses issue of data exchange. During so called task composition step the data processed on each processor has to be distributed to all other processors. In the paper we introduce a multiphase data exchange used for information dissemination in LA parallel computations. For the assumed processing system model we derive the analytical formulae for the task composition completion time in balanced and non-balanced data distribution.