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An Introduction to Shape Schema Grammars

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  • Robert Woodbury

Abstract

Shape schema grammars generalize parametric shape grammars so that both rules and the objects to which they apply are expressed with shape schemata. This paper defines shape schema grammars. It starts with a notation for schemata in general and shape schemata in particular. Schema equality is shown to have at least three possible definitions, of which schema consistency is the most useful. A limited notion of shape schema maximality potentially reduces the size and redundancy of a given schema. Shape schema subpart is a multifunction returning all of the possible ways that one shape schema can be embedded in another. Shape schema difference and addition complete the basic mathematical operations over shape schemata required to define shape schema rules, grammars and languages.

Suggested Citation

  • Robert Woodbury, 2016. "An Introduction to Shape Schema Grammars," Environment and Planning B, , vol. 43(1), pages 152-183, January.
    • Handle: RePEc:sae:envirb:v:43:y:2016:i:1:p:152-183
    DOI: 10.1177/0265813515610671
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