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Relevance is an underlying concept in the field of Information Science and Retrieval. It is a cognitive notion consisting of several different criteria or dimensions. Theoretical models of relevance allude to interdependence between these dimensions, where their interaction and fusion leads to the final inference of relevance. We study the interaction between the relevance dimensions using the mathematical framework of Quantum Theory. It is considered a generalised framework to model decision making under uncertainty, involving multiple perspectives and influenced by context. Specifically, we conduct a user study by constructing the cognitive analogue of a famous experiment in Quantum Physics. The data is used to construct a complex-valued vector space model of the user's cognitive state, which is used to explain incompatibility and interference between relevance dimensions. The implications of our findings to inform the design of Information Retrieval systems are also discussed.

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This article presents a general framework that allows irrational decision making to be theoretically investigated and simulated. Rationality in human decision making under uncertainty is normatively prescribed by the axioms of probability theory in order to maximize utility. However, substantial literature from psychology and cognitive science shows that human decisions regularly deviate from these axioms. Bistable probabilities are proposed as a principled and straight forward means for modeling (ir)rational decision making, which occurs when a decision maker is in “two minds”. We show that bistable probabilities can be formalized by positive-operator-valued projections in quantum mechanics. We found that (1) irrational decision making necessarily involves a wider spectrum of causal relationships than rational decision making, (2) the accessible information turns out to be greater in irrational decision making when compared to rational decision making, and (3) irrational decision making is quantum-like because it violates the Bell–Wigner polytope.

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