Semantics of communicated data can lead to conclusions with varying degrees of priorities. Depending on the interests of the communicating parties, some facts lead to conclusions that carry a high risk when ignored, and others may not be worth the resources to share the facts leading to those uninteresting conclusions. This paper studies the worst-case semantic data compression problem for sharing facts that lead to conclusions with such varying priorities. We establish the performance bounds by utilizing the partial dependencies between the ideas and the priority distributions on the conclusions. We show that multiple term descriptions of the facts and conclusions improve the compression performance when combined with judicious partitioning of the fact space.