Quantum Analogical Modeling with Homogeneous Pointers

Abstract: Quantum Analogical Modeling (QAM) works under the assumption that the correct exemplar-based description for a system of behavior minimizes the overall uncertainty of the system. The measure used in QAM differs from the traditional logarithmic measure of uncertainty; instead QAM uses a quadratic measure of disagreement between pairs of exemplars. (This quadratic measure parallels the squaring function holding between the amplitude and the probability for a state function in quantum mechanics.) QAM eliminates all supracontexts (contextual groupings of exemplars) that fail to minimize the number of disagreements. The resulting system thus distinguishes between homogeneous and heterogeneous supracontexts and uses only exemplars in homogeneous supracontexts to predict behavior. This paper revises earlier work on QAM (in 2005) by showing that homogeneity for a supracontext can be most simply determined by discovering whether there are any heterogeneous pointers between any of the supracontext's exemplars. A pointer for a pair of exemplars is heterogeneous whenever those two exemplars are found in different subcontexts of the supracontext and take different outcomes.