the collections p1; p2; p3; q1; q2  and  r1; r2; s1  would be formed.  If a property appears in the start or finish of both rules then a single collection will be formed from the two rules.

The last stage in the rule construction phase is to identify the basis for the construction of property and attribute spaces. This is done by uniting the left and right hand sides of the rules. Uniting forms collections of properties that each seed a unique property or attribute ssss treatment of both kinds of space is identical at this stage. The enablers of the rules are ignored during this process. We do not wish to make enablers automatically fall into the same property spaces as the states in the transformations they enable. This could result in incorrect assignment of properties to property and attribute spaces since enablers only facilitate, and do not participate in, state transformations. The output of this phase is the collection of rules, with some properties marked as attributes, and the property space seeds formed from the uniting process. All properties that remain unassigned at this stage are used to seed separate attribute spaces, one for each such property.

The role played by the second phase of PRS construction is to postpone commitment to the uniting of collections of properties so that the possibility of objects, which can have these properties, being associated with different property spaces is left open for as long as possible. It may be that consideration of other schemas provides enough information for this possibility to be eliminated, as in the following abstract example, but we support as much type discrimination as possible in the earlier phases of analysis. We consider this simple example to illustrate the problem. 2.3.1 POSTPONING PROPERTY SPACE AMALGAMATION
Given a domain description containing the following operator schema:

| op1(X,Y,Z)   |                   |
|--------------|-------------------|
| Pre:         | p(X, Y), q(X, Y)  |
| Ad:          | p(X, Z), q (X, Z) |
| Del:         | p(X, Y), q(X, Y)  |

$$\mathrm{t\,\,he\,\,\,PRS};$$

| precs :                | Pl, 91   |
|------------------------|----------|
| deleted_precs :        | P1: 91   |
| add_elements :  P1; 91 |          |

will be constructed, during the first phase, for X. The properties pi and qi are bound togetherin this PRS, and the resulting rule would be:
Pl : 91

## Pl; 91

which forces objects that can have property p1 to occupy the same property space as objects that can have property qi. Since this PRS models the exchange of pi we will split it, and replace it with two new PRSs:
precs :
Pl, 91 deleted_precs :
P 1 add_elements :
P 1