DERIVATION

Derived representations are characterized by their isomorphic relationship and the ability of one each representation to be transformed into another. In short each representation can be fully constructed from its derivation. The features grammars of [Finger & Safier 90] are examples of the derivation class of transformation. These grammars generally arise from Chomsky's work in generative grammars.

As an example, the topological graphs of walls, and edges allow for a derivation of a particular feature, while the given feature allows for a derivation of the topology graph. Transformations within the same system provides for both the identification of and the generation of features.

No information is lost in the transformation. Although information required from one representation may not be explicit, it can at least be inferred from the other because there is a one to one mapping, although perhaps through repeated application of grammatical rules. The transmutability of the derivation transformation can be exemplified by the following:

(EQ 12)

On an applied level, the availability of information does not mean that there are explicit links between elements of one representation and elements of the other. Rather, one representation serves as an icon of the other. The representation has the constituents essential or necessary for completeness.