These are used to seed property spaces. We first associate the rules with these property s pace seeds, resulting in the following assignment:

at 1 , i n 1 ini, fuelled i at l at 1 at 1 fuelled」, unfuelled 1 fuelled     unfuelled at l location 1 null at 2, at 2 at շ null at 2 at 2 null in 2 null in 2 at l
The last two spaces have been converted into attribute spaces by their association with attribute transition rules. The resulting spaces can now be supplemented with domain constants and their legal states. We first identify the subset of the legal states of the domain objects that are identifiable from the initial state. We do not use the goal state to provide further information about the properties of objects. The goal state might be unachievable because objects cannot obtain the required properties. This would invalidate TIM's analysis of the domain. In the initial state the rocket has properties at 1 and fuelled 1 , the package has property at 1, London has property at 2 and Paris has property at 2. Using this information we associate domain constants with the developing state and attribute spaces to obtain:
at 1 , in 1 fuelled」, unfuelled」
at 2 in2

$$\begin{array}{r l r l r l r l}{a t_{1}}&{{}}&{i n_{1},\,f u e l l e d_{1}}&{a t_{1}}&{a t_{1}}&{}&{r o c k e t,\,p a c k a g e}\\ {a t_{1}}&{f u e l e d_{1}}&{n u f e l e d_{1}}&{}&{}&{r o c k e t}\\ {l o c a t_{1}}&{n u l l}&{a t_{2},\,a t_{2}}&{a t_{2}}&{}&{n u l l,}&{L o n d o n,\,P a r i s}\\ {a t_{2}}&{n u l l}&{}&{}&{}&{}&{}&{}&{}&{}\\ {a t_{1}}&{n u l l}&{i n_{2}}&{}&{}&{}&{}&{}&{}&{}&{}\end{array}$$
$$\begin{array}{l}a t_{1}\\ a t_{1}\\ l o c a\end{array}$$  $$\begin{array}{l}a t_{1}\end{array}$$ . 
The next step is to add the legal states of these objects, which are identifiable so far, to the property spaces. This results in the following structures, the first two of which can be extended by inference (as will be explained) into completed property spaces. The last two will be extended into completed attribute spaces by the addition of objects that can potentially acquire the associated attributes (also described below).

 $\,at_1\,,\,in_1\\\\\\fuelled_1,\,unfuelled_1\\\\\\ at_2\\\\\\i n_2$
 $\begin{matrix}at_1&in_1,\:fuelled_1&at_1&at_1\\ \\ at_1&fuelled_1&unfuelled_1\\ \\ location_1&null&at_2,\:at_2&at_2&null,\\ &at_2&null\\ at_1&null&in_2\\ \end{matrix}$
$$\begin{array}{l}at_{1}\end{array}$$ = $$\begin{array}{l}at_{1}\end{array}$$ = $$\begin{array}{l}lcc\end{array}$$ = $$\begin{array}{l}at_{1}\end{array}$$
rocket, package

| at l          |
|---------------|
| rocket        |
| fuelled,      |
| London, Paris |

The last stage in the construction of the two property spaces is to add any states that can be inferred as reachable, via transition rules, by objects in the property spaces. For example, packages can go from being at 1 to being in 1 , by application of the rule at 1 in 1 ,
and since that rule is available in the property space to which package belongs, and at 1 is one of the legal states in that property space, we add in 1 as a further legal state. In general, we construct the extension by, for each state in the space, identifying applicable rules and, for each rule, creating a new state by removing the properties in the start of the