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Structured representations in a quantum probability model of similarity

Pothos, E. M. & Trueblood, J. S. (2015). Structured representations in a quantum probability model of similarity. Journal of Mathematical Psychology, 64-65, pp. 35-43. doi: 10.1016/


Recently, Busemeyer et al. (2011) presented a model for how the conjunction fallacy (Tversky & Kahneman, 1983) emerges, based on the principles of quantum probability (QP) theory. Pothos et al. (2013) extended this model to account for the main similarity findings of Tversky (1977), which have served as a golden standard for testing novel theories of similarity. However, Tversky’s (1977) empirical findings did not address the now established insight that, in comparing two objects, overlap in matching parts of the objects tends to have a greater impact on their similarity, than overlap in non-matching parts. We show how the QP similarity model can be directly extended to accommodate structure in similarity comparisons. Smolensky’s et al.’s (2014) proposal for modeling structure in linguistic representations, with tensor products, can be adapted ‘as is’ with the QP similarity model. The formal properties of the extended QP similarity model are analyzed, some indicative fits are presented, and, finally, a novel prediction is developed.

Publication Type: Article
Additional Information: NOTICE: this is the author’s version of a work that was accepted for publication in Journal of Mathematical Psychology. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Journal of Mathematical Psychology, Volumes 64–65, February–April 2015,
Publisher Keywords: Quantum probability theory; Similarity; Representation
Subjects: B Philosophy. Psychology. Religion > BF Psychology
Q Science > QA Mathematics
Departments: School of Health & Psychological Sciences > Psychology
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