Abstract
We present the fundamentals of the quantum theoretical approach we have developed in the last decade to model cognitive phenomena that resisted modeling by means of classical logical and probabilistic structures, like Boolean, Kolmogorovian and, more generally, set theoretical structures. We firstly sketch the operational-realistic foundations of conceptual entities, i.e. concepts, conceptual combinations, propositions, decision-making entities, etc. Then, we briefly illustrate the application of the quantum formalism in Hilbert space to represent combinations of natural concepts, discussing its success in modeling a wide range of empirical data on concepts and their conjunction, disjunction and negation. Next, we naturally extend the quantum theoretical approach to model some long-standing `fallacies of human reasoning', namely, the `conjunction fallacy' and the `disjunction effect'. Finally, we put forward an explanatory hypothesis according to which human reasoning is a defined superposition of `emergent reasoning' and `logical reasoning', where the former generally prevails over the latter. The quantum theoretical approach explains human fallacies as the consequence of genuine quantum structures in human reasoning, i.e. `contextuality', `emergence', `entanglement', `interference' and `superposition'. As such, it is alternative to the Kahneman-Tversky research programme, which instead aims to explain human fallacies in terms of `individual heuristics and biases'.
Highlights
(i) ‘Probability judgment errors’: people judge the probability of the conjunction ‘A and B’ of two events A and B as higher than the probability of one of them, violating in this way the ‘monotonicity law of Kolmogorovian probability’
We present the fundamentals of the quantum theoretical approach we have developed in the last decade to model cognitive phenomena that resisted modeling by means of classical logical and probabilistic structures, like Boolean, Kolmogorovian and, more generally, set theoretical structures
Expected utility theory (EUT), which provides the normative foundations of rational behavior under uncertainty, guarantees that decision-makers should behave as if they maximized EU with respect to a Kolmogorovian probability measure formalizing their subjective uncertainty about the world [2]
Summary
Researchers in cognitive and social science have assumed for many years, often implicitly, that human judgment and decision-making under uncertainty can be modeled by means of set theoretical structures, i.e. sets and operations between sets. Expected utility theory (EUT), which provides the normative foundations of rational behavior under uncertainty, guarantees that decision-makers should behave as if they maximized EU with respect to a Kolmogorovian probability measure formalizing their subjective uncertainty about the world [2] This classical paradigm has been seriously challenged by a number of paradoxical findings in cognitive psychology, revealing that classical structures are generally unable to model concrete human decisions. We show that any conceptual entity, that is, a single concept, a conceptual combination, a proposition, or a more complex decision-making entity, can be abstractly described in terms of the operationally defined notions of ‘states’, ‘contexts’, ‘properties’, ‘measurements’ and ‘outcome probabilities’, and that impressive analogies recur between the operational description of measurement processes and the effects of context on quantum and conceptual entities This indicates that the quantum formalism and its quantum probability structure are natural candidates to model cognitive phenomena. The Brussels quantum modeling approach to conceptual entities was the starting point for the development of a quantum theoretical approach to ‘meaning entities’ that can be associated with documents and texts, like those of the World Wide Web, which is presented in [26]
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