In our earlier work, we have developed a theory of Model-Based Analogy based on Structure-Behavior-Function models of causal mechanisms and physical systems. The IDeAL system [Bhatta and Goel1997], for example, transfers generic teleological mechanisms from a source analog to a target problem to address novel design problems. The ToRQUE system [Griffith et al.2000] uses generic structural transformations to mutate a target problem or a source analog to construct analogies. Galatea builds on the above theory of model-based analogy in that in it too relies on the core idea of generic transformations. Thus, while the analogical process in Galatea is similar to that in IDeAL, the content of its generic transformations is visual as opposed to teleological or structural. ToRQUE's structural knowledge captures only a small subset of visual knowledge. In contrast Galatea has information about the location and appearance of objects in a particular simage: the fortress is not just connected to the road, it is in the center of the simage; the path is not just on the road, it is a thick line. These additional features enable the initial analogical mapping between simages without causal knowledge because the simages representing the two analogs are similar when described visually.
Like Galatea, LetterSpirit is a model of analogical transfer [McGraw and Hofstadter1993]. It takes a stylized seed letter as input and outputs an entire font that has the same style. It does this by determining what letter is presented, determining how the components are drawn, and then drawing the same components of other letters the same way. Like Galatea, the analogies between letters are already in the system: the vertical bar part of the letter ``d'' maps to the vertical bar in the letter ``b,'' for example. A mapping is created for the input character. For example, the seed letter may be interpreted as an ``f'' with the cross-bar suppressed. When the system makes a lower-case ``t,'' by analogy, it suppresses the crossbar.
It is not at all clear that LetterSpirit is applicable to other domains (such as the fortress/tumor problem) in part because there is little distinction between its theory and the implementation that works for letters. In contrast, one can see how Galatea might be applied to the font domain: The stylistic guidelines in LetterSpirit, such as ``crossbar suppressed'' are like the visual transformations in Galatea: it would be a transformation of removing an element from the image, where that element was the crossbar and the image was a prototype letter ``f.'' Then the transformation could be applied to the other letters one by one. We conjecture that our theory has more generality than LetterSpirit.
Galatea does not generate the analogical mapping, but other systems, that create mappings with visual information, have shown that it can be done. The VAMP systems are analogical mappers as well [Thagard et al.1992]. VAMP.1 uses a hierarchically organized symbol/pixel representation. It superimposes two images, and reports which components have overlapping pixels. VAMP.2 represented images as agents with local knowledge. Mapping is done using ACME/ARCS [Holyoak and Thagard1997], a constraint satisfaction connectionist network. The radiation problem mapping was one of the examples to which VAMP.2 was applied.
The Structure Mapping Engine, or SME [Falkenhainer et al.1990] finds the best mapping of elements between two domains. But SME typically is applied to instances where the situations are represented as having causal and structural knowledge. SME has been applied to visual knowledge in a system called MAGI [Ferguson1994], which takes visual representations and uses SME to find examples of symmetry and repetition in a single image.
Like Galatea, MAGI and the VAMPs use visual knowledge. But unlike Galatea their focus is on the creation of the mapping rather than on transfer of a solution procedure. MAGI's and Galatea's theories are compatible: a MAGI-like system might be used to create the mappings that Galatea uses to transfer knowledge. The theory behind the VAMPs is incompatible because they use a different level of representation for the images.
Galatea has also been applied to the case study of James Clerk Maxwell's creation of his electro magnetic theory. According to Nersessian's Cognitive-Historical Analysis [Nersessian1995], Maxwell used analogical transfer to resolve a problem with his mental model of electro-magnetism. The transfer was mediated by a generic abstraction, and the abstraction was created, retrieved, and instantiated using visual representations and reasoning.
Galatea so far has been substantiated for only two examples: Duncker's fortress/tumor problem and Maxwell's case study. In the future, we will extend Galatea to cover many more problems, and expand it to use, in addition to simages, bitmap images, which we believe will be important for changing representations when symbol mismatches make analogical mapping difficult.