Cognitive reading models are typically assessed based on how well they describe, explain, and - in the case of computer simulations - also simulate human behavior. However, cognitive models also represent characteristics of the material that is to be processed. This raises two questions: Which features of writing are represented in cognitive reading models? Which properties are considered universal? Based on a notation-theoretical framework, universal and specific characteristics of writing and writing types are identified using the example of the German alphabet and the Chinese characters (Kanji) used in Japan. Consequences for modeling cognitive processing are derived from this. Finally, the two-way model and the connectionist triangle model of reading are evaluated against the theoretical requirements of writing.