The landscape of analogy research can be cut in different ways. I will discuss some major theories in the field with respect to 1) their approach to matching and similarity, 2) their structure versus content emphasis, and 3) their emphasis on particular parts of the analogical process. The models I will discuss are my own, ACME (Holyoak & Thagard, 1989b), MBA (Bhatta & Goel, 1997c), SME (Falkenhainer et. al., 1990; Gentner 1983), derivational analogy (Veloso & Carbonell, 1993; Carbonell, 1986), case-based reasoning (Kolodner, 1993; Hammond, 1990), Copycat (Hofstadter & Mitchell, 1995) and HACKER (Sussman, 1975).
Matching and similarity issues concern how analogs are mapped, retrieved and processed in transfer. Approaches can be classified into five themes. First, attributes of analogs can be encoded according to numeric values. Similarity can then be defined as some distance measure in a multi-dimensional space (described in Winston, 1992, p24). Second, attributes can be represented in terms of non-numeric features to be matched exactly. Proteus, SME, ACME, Copycat, derivational analogy, case-based reasoning, and HACKER fall into this category. Third, structure-based similarity has a focus on the relational structure of the analogs. SME and ACME both rely heavily on both features and relational structure. Some systems guide similarity evaluation with the agent's goals, the fourth theme. MBA relies heavily on the goals, as well as different methods for the same task. ACME has a heuristic for favoring elements and propositions relevant to the goal in retrieval and mapping. In contrast, SME's mapper has no notion of the goal. Proteus does not emphasize the agent's goals. Fifth, Some systems use stored abstractions to guide similarity. Certain MBA systems do, and Proteus uses visual abstractions to guide similarity. SME uses very small abstractions in the form of variablized functions.
The next cut is that of content-based theories and process-based theories. Proteus, Copycat, and MBA (and its SBF and TMK representation languages) rely on knowledge but also make theoretical claims about how knowledge is structured. Content-based theories create typologies of content. SME and ACME, for example, do not do this. For example, an SME model might represent the sun as having the property hot, but there is nothing in SME's theory that determines that it must be represented this way. The emphasis is on the processing whatever the content might be. In contrast, my theory has a limited language of primitives of which visual representations are composed. Enforcing this language for every example used and tying it to the process theory counters the argument that the systems works because the representation was example-specific.
Some theories of analogy, such as CBR, endeavor to explain similarities of within-domain examples, and others focus on cross-domain similarity. In CBR, the case library is assumed to be large enough such that a case similar to the one you are working with can be retrieved. My theory, MBA, SME, and ACME all focus on cross-domain analogy. As a result mapping and transfer are difficult problems, and these systems focus on them.
HACKER represents problems and solution states. CBR represents problems, solution states, and an evaluation of the outcome. SME, ACME, and MBA focus on the problem, the solution, and a model of the systems in question. As opposed to a more traditional approach to problem solving, these systems do explanation and model construction. Derivational analogy represents the problem, the solution state, and the trace of the problem-solving procedure. My theory is closest to this, in that the problem, solution procedure, intermediate states, and the solution state are represented. Like Derivational Analogy, my theory focuses on transfer.
Traces, called derivations, are scripts of the steps of problem solving, along with justifications for why the steps were chosen over others. One way my work differentiates itself is that in derivational analogy, the nv-states are not saved, as such, only the record of the changes made to them. This means that the nv-states can be inferred, but are not explicitly present in memory. Functionally, this means that retrieval based on those states is not possible, where in my theory, it is possible to retrieve a subsection of a problem solving solution sequence.
There are computational theories of analogical problem solving that use non-visual representations (dealing with, for example, actions, events and causality), but there are none that use visual representations.