is interpreted to mean that each of the properties in the collection can be satisfied as many times as they appear in the collection. The comma is therefore used to separate the elements of a bag. We use to denote bag union, to denote bag difference, to denote bag intersection and to denote bag inclusion.

Definition 10 A Property Relating Structure (PRS) is a triple of bags of properties.

The first stage of the algorithm constructs aset of transition rules from aset of operator schemas. Each operator schemais analysed with respect to each parameterin turn and, for each parameter, a PRS is built. The first bag of properties is formed from the preconditions of the schema, and the number used to form the property is the argument position of the parameter being considered. For example, if the precondition is on (X,Y), and the parameter being considered is X, the property formed is on 1.  This bag, called precs, contains the enablers that will be used in the formation of the transition rules. The second bag, called deleted_precs, of properties is formed from all of the preconditions that appear on the delete list of the schema (with respect to this same parameter). The third bag, called add_elements, contains the properties that can be formed from the add list of the schema. The PRS contains no deleted elements component it is assumed that every element on the delete list of a strips operator appears in the precondition list. This is a reasonable restriction given that strips operators do not allow the use of conditional effects. It is further assumed that every pair of atoms on the delete list of a schema will be distinct for all legal instantiations of the schema. This does not constitute a significant restriction since operator schemas can always be easily rephrased whenever this condition is violated.

We now consider the process by which PRSs are constructed. Given the schema:

| drive( X,Y,Z)   |
|-----------------|
| Pre:            |
| Ad:             |
| Del:            |

$$\begin{array}{r l}{\operatorname{at}{\left(\mathrm{X},\mathrm{Y}\right)},}&{{}{\mathrm{f u e l l e d\left(X\right)}},}&{{}{\mathrm{l o c a t i o n\left(Z\right)}}}\\ {\operatorname{at}{\left(\mathrm{X},\mathrm{Z}\right)},}&{{}{\mathrm{u n f u e l l e d\left(X\right)}}}\\ {\operatorname{at}{\left(\mathrm{X},\mathrm{Y}\right)},}&{{}{\mathrm{f u e l l e d\left(X\right)}}}\end{array}$$

and considering the parameter X, the following PRS will be built:
PRS 1

$$\begin{array}{l l}{{p r e c s:}}&{{a t_{1},\,f u e l l e d_{1}}}\\ {{d e l e t e d_{-}p r e c s:}}&{{a t_{1},\,f u e l l e d_{1}}}\\ {{a d d_{-}e l e m e n t s:}}&{{a t_{1},\,\,u n f u e l l e d_{1}}}\end{array}$$

By considering the parameter Y we obtain:
PRS 2

$$\begin{array}{l}{{p r e c s:}}\\ {{d e l e t e d_{-}p r e c s:}}\\ {{a d d_{-}e l e m e n t s:}}\end{array}$$
$$a t_{2}$$ $$a t_{2}$$

and by considering the parameter Z we obtain: