Uncertainty management has been a challenging issue in AI and database research. Logic database programming with its declaration advantage and ist top-down and bottom-up query processing techniques has been an attractive formalism for represening and manipulating uncertain information, and momerous frameworks with uncertainty has been proposed. These proposals address fundamental issues of modeling, semantrics, query processing and optimization, however, one important issue with remains unaddressed is efficient implementation of such frameworks. In this paper, we illustrate that standard semi-naive evaluation method does not have a counterpanrt in general in these frameworks. We then propose a desired semi-naive algorithm, which extends the corresponding standard mehod, and establish its equvalence with the naive method with uncertaninty. We implemented the algorithm and conduced numweoua tests. Our experimental results indicate that the propused techniques is practical and supports efficient fixpoint computation with uncertainty. We beleave that the method is also useful in a source general context of expoint computation with agregations