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However, if desired, a formal proof can be derived on the basis of the algebraic interpretations of a rule's constituent formulae. The set of interpretations of a rule's condition part form a small system of simultaneous constraint equations, from which the equations that express the interpretation of the conclusion part are easily derived [16]. As the above examples show, the rules considered here have been designed with an orientation towards two-dimensional (20) geometries, according to the presupposition that man-machine communication takes place via dimensioned drawings.

1, the parallelism of T7 and T9 with each other is preferred over the perpendicularity of T2 and T7 , which has a lower visibility. Besides constituting a proof procedure, the chain of recorded inferences can also be interpreted as a construction plan that specifies a step-bystep construction of the geometric elements by elementary operations. Through execution of this plan, different variants of the prototype geometry can be generated when desired. All these variants conform exactly to the model constraints.

In the language-oriented model, not only metric but also all structural relationships are explicitly represented, including both constraints and incidental relationships, if present. Information that is explicitly encoded in the data structure becomes immediately available through simple interrogation. For example, the algorithm for generating all line segments consists of a navigation through the data structure with iteration of the following steps: 1. 2. 3. 4. Find the next line segment and get its name, L.

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