Title: Semantic Prior for Weakly Supervised Class-Incremental Segmentation. Abstract: Class-incremental semantic image segmentation assumes multiple model updates, each enriching the model to segment new categories. This is typically carried out by providing pixel-level manual annotations for all new objects, limiting the adoption of such methods. Approaches which solely require image-level labels offer an attractive alternative, yet, such annotations lack crucial information about the location and boundary of new objects. In this paper we argue that, since classes represent not just indices but semantic entities, the conceptual relationships between them can provide valuable information that should be leveraged. We propose a weakly supervised approach that leverages such semantic relations in order to transfer some cues from the previously learned classes into the new ones, complementing the supervisory signal from image-level labels. We validate our approach on a number of continual learning tasks, and show how even a simple pairwise interaction between classes can significantly improve the segmentation mask quality of both old and new classes. We show these conclusions still hold for longer and, hence, more realistic sequences of tasks and for a challenging few-shot scenario.