Information incompleteness is a major data quality issue which is amplified by the increasing amount of data collected from unreliable sources. Assessing the completeness of data is crucial for determining the quality of the data itself , but also for verifying the validity of query answers over incomplete data. While there exists an important amount of work on modeling data completeness, deriving this completeness information has not received much attention. In this work, we tackle the issue of efficiently describing and inferring knowledge about data completeness w.r.t. to a complete reference data set and study the use of a pattern algebra for summarizing the completeness and validity of query answers. We describe an implementation and experiments with a real-world dataset to validate the effectiveness and the efficiency of our approach.