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This study offers two key contributions. Firstly, it introduces the concept and framework of "section grammars" (SecG), which is derived from Stiny's shape grammars. Secondly, it investigates the potential of SecG in generating existing and alternative section layouts for ancient underground cities. The case study focuses on Derinkuyu, which is located in Cappadocia, Turkey. The study thoroughly examines the components of the Derinkuyu underground city, presents its parameters, and explains the rules based on the relations between these components. The study employs these elements and rules to generate an existing satellite city as well as a new synthetic satellite city. Finally, the paper discusses the outcomes of implementing the SecG framework. This study contributes to shape grammar studies by integrating the subtractive (carving) approach and the topological relations observed in underground cities into the proposed framework.