Analogical reasoning has been modelled using classical models of cognition, and more recent neural network paradigms. Many of these models have not investigated the representational structures on which their respective knowledge domains are built. Most models emphasise the importance of relations, but without a clear definition of what relations are. Subsequently, much of the power in these models lies in the processes utilising the representations, rather than in the dynamics of the representational systems. Consequently, while analogy is a creative process, many of the models lack creative ability.
In this thesis, the theory of relations was developed substantially. A generative theory of analogy based on Spearman's (1923) Eduction of Relations and Eduction of Correlates theory, was then developed using the new theory of relations. The 'generative theory' was then specified and implemented in a neural net model, Net AB. The structure of the model was designed so as to model eduction of relations in one part and eduction of correlates in another, and to produce solutions to analogies. The model was also based on Rumelhart and Abrahamson's (1973) vector addition and subtraction model of analogy (the parallelogram model), which could also be viewed as an eduction model.
NetAB comprised two feedforward nets. The first net, the binding net (NetB), took arguments for relations as inputs and produced labels for the relations as outputs. In the hidden layer, NetB created reduced internal representations for relations, called 'bindings'. NetB was successfully trained to learn bindings and labels for relations between animals. It was then able to generalise to unseen relations between animals. The second net, the application net (NetA) took the NetB bindings and applied them to target element in an analogy problem to find a solution. In the analogy a : b :: c :?, NetB would create a binding for the aRb relation, and then NetA would apply that binding to c, to produce a solution, d. NetA was trained to apply aRb bindings to a to produce b. After training, it could then apply any relation from the base to the target. The aim of the eduction model was that the aRb relation be the same as the cRd relation. However, in the eduction model, this similarity was not pre-specified, but generated by the eduction processes of NetAB.
Two human experiments were performed. The first gathered data to be used as inputs to the net. The second tested the NetAB solutions against human analogy solutions. This two-stage experimental paradigm was based on the method of Rumelhart and Abrahamson (1973). The data allowed NetAB to take as inputs points from subjects' conceptual space for animals, constructed using a multi-dimensional scaling (MDS) technique. NetAB produced points in conceptual space as solutions to analogies. The first experiment was a typical MDS rank-ordering study. Subjects were given 18 animals, and for each animal, were asked to rank order the similarity of all the other animals. From this data, each subject's MDS conceptual space for animals was constructed. These points were then used as inputs for NetAB. The second experiment gave subjects 30 randomly created analogies in the form a is to b as c is to ?, and subjects were asked to select the missing element from all 18 alternatives.
Human analogy solutions were used as the criteria for assessing both the NetAB model and the parallelogram model as models of human analogical thought. In addition, the ability of NetAB to model the parallelogram model was assessed. Model solutions, which varied from +1 to -1 on each dimension, were deemed to be correct if they fell less than .5 away from normalised human solutions. In addition, the target vectors (the difference between the solution and the target element) for each model were compared with the human target vectors using correlations between vectors.
The results showed that NetAB was able to model the parallelogram model. Both models were able to produce solutions and target vectors similar to humans, but only along one dimension at a time. The results were better (though not significantly so) along the size dimension. This result suggested that the 3-D MDS space limited the accuracy of the models, and has consequences for future models of analogy. NetAB target vectors were more correlated with human vectors than were parallelogram vectors (though the differences between models was not significant). This result was explained in terms of the different functions performed by NetAB and the parallelogram model.
The binding units of NetB kept information about the relative differences between arguments of relations; i.e. ordinal information rather than interval information. This ordinal information was applied to the target element to find a solution. The ordinal differences seemed to reflect human processing better than the interval differences used by the parallelogram model. This result has implications for the theory of relations and of analogy.
NetB was found to be capable of implementing most of the components of relations, as specified in the generative theory. The main deviation from the theory was based on the representational scheme created for bindings. This positional representation was found to be somewhere between a perceptual and a symbolic representation. NetA was found to be capable of applying bindings to target elements as specified in the generative model. The components of NetAB were shown to be positive instantiations of the generative theory of relations and of analogy. NetAB was able to model eduction of relations and eduction of correlates, and to illustrate how these processes can be used to model creative analogy.
The results have implications for future theories and models of relations and of analogy. Relations no longer need to be pre-wired, as they can be modelled such that they can be learned. Relations can be educed during problem solving, and applied from the base to the target. These two processes need to be explored futher as the basic processes involved in analogical reasoning. Dynamic creation and use of symbolic representations for relations is possible using a neural network paradigm. Further reseach is required to find symbolic representations for bindings, and context-dependent representations for relations.