The thesis is that quantum probability theory provides a more accurate and powerful account of certain cognitive processes than classical probability theory, and this work discusses ways in which QP and CP theories converge.
Abstract:
Classical (Bayesian) probability (CP) theory has led to an influential research tradition for modeling cognitive processes. Cognitive scientists have been trained to work with CP principles for so long that it is hard even to imagine alternative ways to formalize probabilities. However, in physics, quantum probability (QP) theory has been the dominant probabilistic approach for nearly 100 years. Could QP theory provide us with any advantages in cognitive modeling as well? Note first that both CP and QP theory share the fundamental assumption that it is possible to model cognition on the basis of formal, probabilistic principles. But why consider a QP approach? The answers are that (1) there are many well-established empirical findings (e.g., from the influential Tversky, Kahneman research tradition) that are hard to reconcile with CP principles; and (2) these same findings have natural and straightforward explanations with quantum principles. In QP theory, probabilistic assessment is often strongly context- and order- dependent, individual states can be superposition states (that are impossible to associate with specific values), and composite systems can be entangled (they cannot be decomposed into their subsystems). All these characteristics appear perplexing from a classical perspective. However, our thesis is that they provide a more accurate and powerful account of certain cognitive processes. We first introduce QP theory and illustrate its application with psychological examples. We then review empirical findings that motivate the use of quantum theory in cognitive theory, but also discuss ways in which QP and CP theories converge. Finally, we consider the implications of a QP theory approach to cognition for human rationality.
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Q1. What have the authors contributed in "Can quantum probability provide a new direction for cognitive modeling?" ?
The authors first introduce QP theory and illustrate its application with psychological examples. The authors then review empirical findings that motivate the use of quantum theory in cognitive theory, but also discuss ways in which QP and CP theories converge. Finally, the authors consider the implications of a QP theory approach to cognition for human rationality.
Q2. What are the future works mentioned in the paper "Can quantum probability provide a new direction for cognitive modeling?" ?
There is little doubt that extensive further work is essential before all aspects of QP theory can acquire psychological meaning. In fact, the authors argue that the quantum approach to cognition embodies all the characteristics of good cognitive theory: it is based on a coherent set of formal principles, the formal principles are related to specific assumptions about psychological process ( e. g., the existence of order/context effects in judgment ), and it leads to quantitative computational models that can parsimoniously account for both old and new empirical data. Rather, quantum theory provides many theoretical and practical advantages, and its applicability to psychological explanation should be further considered.
Q3. What is the only system that works in physics?
For the real, noisy, confusing, ever-changing, chaotic world, QP is the only system that works in physics and, the authors strongly suspect, in psychology as well.
Q4. What is the reason why probability is interpreted as similarity?
Because in QP theory probability is computed from the overlap between a vector and a subspace, it is naturally interpreted as similarity (Sloman 1993).
Q5. What is the example of a holism in memory research?
Another example from memory research is Bruza et. al.’s (2009) application of quantum entanglement (which implies a kind of holism inconsistent with classical notions of causality) to explain associativememoryfindings,which cannot beaccommodated within the popular theory of spreading activation.
Q6. What is the influential demonstration of similarity?
In one of the most influential demonstrations in the similarity literature, Tversky (1977) showed that similarity judgments violate all metric axioms.
Q7. What is the probability of defecting when the opponent is known to cooperate?
the probability of defecting when the opponent is known to cooperate is based on the projection Pparticipant to D |Ψopponent known C〉. But, in the unknown case, the relevant state vector is the superposition 1 2√ |copponent known Dl+ 1 2√ |copponent known Cl.
Q8. What is the effect of deciding that gore is honest?
In other words, deciding that Gore is honest increases the probability that Clinton is judged to be honest as well (and, conversely,deciding that Clinton is honest first, reduces the probability that Gore is judged as honest).
Q9. Who was known to believe that aspects of quantum theory could provide insight about cognitive process?
one of the founding fathers of quantum theory, was known to believe that aspects of quantum theory could provide insight about cognitive process (Wang et al., in press).