This work studies the problem of aggregate query processing over incomplete data based on denotational semantics. Incomplete data is also known as missing values and can be classified into two categories:applicable nulls and inapplicable nulls. Existing imputation algorithms cannot guarantee the accuracy of the query result after imputation. The interval estimation of the aggregate query result is given. This study extends the relational model under the denotational semantic, which can cover all types of incomplete data. A new semantic of aggregate query answers over incomplete data is defined. Reliable answers are interval estimations of the ground-truth query results, which can cover the ground-truth results with high probability. For SUM, COUNT, and AVG queries, linear approximate evaluation algorithms are proposed to compute reliable answers. The extended experiments on the real datasets and synthetic datasets verify the effectiveness of the method proposed in this study.