We introduce the concept of Procedural Content Generation via Knowledge Transformation (PCG-KT), a new lens and framework for characterizing PCG methods and approaches in which content generation is enabled by the process of knowledge transformation -- transforming knowledge derived from one domain in order to apply it in another. Our work is motivated by a substantial number of recent PCG works that focus on generating novel content via repurposing derived knowledge. Such works have involved, for example, performing transfer learning on models trained on one game's content to adapt to another game's content, as well as recombining different generative distributions to blend the content of two or more games. Such approaches arose in part due to limitations in PCG via Machine Learning (PCGML) such as producing generative models for games lacking training data and generating content for entirely new games. In this paper, we categorize such approaches under this new lens of PCG-KT by offering a definition and framework for describing such methods and surveying existing works using this framework. Finally, we conclude by highlighting open problems and directions for future research in this area.