We can write the axioms for moving and painting as follows:
Notice that the assignments are made to the terms location(x) and color(x) rather than to simple variables as in (16). In order to avoid contradiction as well as to describe moving and painting, we need axioms that these objects are different. We have axioms
Using situations as frames in this way makes certain commitments that might not be immediately obvious. Consider distance(x1,x2) which is supposed to be some function of location(x1) and location(x2).
We will not want to use c(distance(x1,x2),s), because our axioms would not permit c(distance(x1,x2),s) to change when the locations changed. Instead we use another function value(term,s) and the equations
The effect is to take location(x) and color(x) as primary fluents and distance(x,y) as a secondary fluent whose value is dependent on the values of primary fluents. Deciding what fluents to make primary is an epistemological decision, i.e. it is a feature of the theory being used. clear(x) must also be a secondary fluent.