As in some other theories of analogical problem solving, in my theory problem solving strategies are transferred. Other theories of visual analogy do not do this.
As shown in Figure 4, the possible source analogs are represented as solution procedures connecting knowledge states. In analogical problem solving, transfer is using a source analogy's solution strategy for the target. This can be done with both visual and non-visual representations.
Transfer works as follows: In the mapping stage, a mapping is found between the source and target initial problem states. The manipulation that connects the first to the next knowledge state in the source is transferred to the target. The parts of the target that the manipulation affects are those analogous parts of what get affected in the source.
When this is done with visual representations, transfer of manipulations can work because they are sufficiently abstract such that they can apply equally well to many different elements. For example, a manipulation that moves something can apply to lines as well as circles. This means that the same move manipulation that worked in the source with a circle can work with the line in the target.
This process can repeat unhindered for the entire sequence, transferring the manipulation from the source and generating new knowledge states in the target. Sometimes, however, there can be problems with symbolic mismatches. For example, as discussed above with the fortress/tumor example, trying to transfer the break-up manipulation to the ray will not work because the ray does not have constituent parts.
Visual representations can be used as an intermediate level of abstraction to do plan adaptation. To follow the example, imagine the advancing army gets visually instantiated as a line, and the ray does as well. The manipulation, too, gets visually instantiated as the decompose visual transformation, which applies fairly broadly to visual elements. In the generated visual representation, the transfer of the manipulation occurs without a problem, as decompose can apply equally well to both lines. I call this visual representation an intermediate step because it must be turned back into the non-visual again, because, I assume, ``solving'' the problem in the visual abstraction is really not informative of actions that must be taken in the real world (more on this in the solution evaluation section). When the visual transformation is turned into a manipulation for the ray in the non-visual representation, it becomes a different manipulation: disperse-energy. Because transformations can specify into different actions, strategies can be adapted to new instances, and steps in the problem solving process do not need to be transferred literally.