Analogical Modeling: Exemplars, Rules, and Quantum Computing”, Proceedings of the Twenty-Ninth Annual Meeting of the Berkeley Linguistics Society, edited by Pawel

I begin this paper by outlining the main properties of analogical modeling (AM): $ AM is an exemplar or instance-based system of prediction; it is not a rule-based system nor a neural network. $ AM is a procedural system, not a declarative one; one cannot directly find its predictions within the system itself. Instead, predictions are always made in terms of a given context for which a prediction (or outcome) is sought. $ AM is not a nearest neighbor approach; it does include nearest neighbors in its predictions, but it also regularly uses non-neighbors to make predictions. How-ever, such non-neighbors can be used only under a well-defined, explicit condi-tion of homogeneity. $ No training stage occurs in AM, except in the trivial sense that one must collect exemplars in order to make predictions. There is no setting of parameters nor any prior determination of variable significance. The significance of any combination of variables is always determined in terms of the given context for which we seek a predicted outcome. Each prediction is done Aon the fly@. $ AM has a simple measure of uncertainty that is defined by the number of out-come disagreements between pairs of exemplars. $ AM uses a simple decision principle to determine homogeneity B namely, mini-mize the number of disagreements. No increase in uncertainty is permitted, which means that no analogical analysis will allow any loss of information. $ This definition of homogeneity results in two types of homogeneous spaces in an analogical analysis: (1) the subspace is deterministic in behavior, which means that there will be no disagreements at all within that contextual space and there-fore no a priori limitation on the extent of a deterministic subspace; (2) the sub-space is non-deterministic in behavior, which means that disagreement occurs within the contextual space, but is restricted to one subspace of the entire space. $ The resulting probability of using a particular exemplar depends upon thre