Abstract. The common structure underlying production system formalisms is developed. A variety of production system formalisms are summarized in terms of this structure. The structure is useful both for understanding existing types of production systems and for developing new ones.

The theory of <I>shapes</I> and the <I>subshape</I> relation is the same as the theory of <I>individuals</I> and the <I>part</I> relation.

The conventions used to design Mughul gardens are characterized. These conventions are represented by a parametric shape grammar.

Designs belong to relations.

An algorithmic structure for design is postulated.

Rules of composition can play a decisive role in understanding.

Spatial relations and shape grammars are defined. A spatial relation is specified by a finite number of shapes arranged in a certain way. A shape grammar provides for the recursive generation of arrangements of shapes in terms of given spatial relations. The possible spatial relations between...

A parametric shape grammar that generates the ground plans of Palladio's villas is developed as a definition of the Palladian style. The grammar is applied to generate the plan for the Villa Malcontenta.

The conventions used to construct traditional Chinese ice-ray lattice designs are investigated. Parametric shape grammars are defined for the recursive generation of these patterns.