A. L. Tulupyev

The theory of algebraical Bayesian networks defines a mathematical model of a knowledge pattern as a conjuncts ideal with scalar or interval conjunct probability estimates. Operations of the local probabilistic-logic inference are performed with knowledge patterns. The local probabilistic-logic inference operations system includes consistency verification, reconciliation, a priori inference, evidence propagation (a posteriori inference), knowledge patterns linear combination and linear enclosure. The results of two latter are consistent of their operands are consistent. The operation of consistency verification detects inconsistencies among initial estimates and among those estimates and the set of probabilistic-logic axioms. The operation of initial interval probabilistic estimates reconciliation either does not change them if they are completely consistent, or narrow some or all of them to make consistent the whole estimates set, or outlines the inconsistency of the initial estimates. The operation of a priori inference outputs the narrowest possible estimate of the probability of a propositional formula that does not belong to the knowledge pattern but is constructed with its atoms. The operation of a posteriori inference (or evidence propagation) allows for taking into account the influence of evidence on the estimates of the knowledge pattern elements. The propagation is depicted as a series of hyperbolic programming problems that later render to the corresponding series of linear programming problems