Sortal grammars for urban design: A sortal approach to urban data modeling and generation

Grammar formalisms for design come in a large variety, requiring different representations of the objects being generated, and different interpretative mechanisms for this generation. At the same time, all grammars share certain definitions and characteristics. Building on these commonalities, we consider a component-based approach for building grammar systems, utilizing a uniform characterization of grammars. Sortal representations constitute the components for this approach. They implement a model for representations, termed sorts, that defines formal operations on sorts and recognizes formal relationships between sorts. Each sort defines an algebra over its elements; formal compositions of sorts derive their algebraic properties from their component sorts. This algebraic framework makes sortal representations particularly suited for defining grammar formalisms considering a variety of algebra, and match relations (or interpretative mechanisms). For urban design and simulation, sortal grammars may include, among others, descriptive grammars, shape grammars, GIS-based grammars and any combination thereof.