Interference Effects in Quantum Belief Networks (original) (raw)

The Relation Between Acausality and Interference in Quantum-Like Bayesian Networks

We analyse a quantum-like Bayesian Network that puts together cause/effect relationships and semantic similarities between events. These semantic similarities constitute acausal connections according to the Synchronicity principle and provide new relationships to quantum like probabilistic graphical models. As a consequence, beliefs (or any other event) can be represented in vector spaces, in which quantum parameters are determined by the similarities that these vectors share between them. Events attached by a semantic meaning do not need to have an explanation in terms of cause and effect.

Balanced Quantum-Like Bayesian Networks

Entropy, 2020

Empirical findings from cognitive psychology indicate that, in scenarios under high levels of uncertainty, many people tend to make irrational decisions. To address this problem, models based on quantum probability theory, such as the quantum-like Bayesian networks, have been proposed. However, this model makes use of a Bayes normalisation factor during probabilistic inference to convert the likelihoods that result from quantum interference effects into probability values. The interpretation of this operation is not clear and leads to extremely skewed intensity waves that make the task of prediction of these irrational decisions challenging. This article proposes the law of balance, a novel mathematical formalism for probabilistic inferences in quantum-like Bayesian networks, based on the notion of balanced intensity waves. The general idea is to balance the intensity waves resulting from quantum interference in such a way that, during Bayes normalisation, they cancel each other. Wi...

QuLBIT: Quantum-Like Bayesian Inference Technologies for Cognition and Decision

2020

This paper provides the foundations of a unified cognitive decision-making framework (QulBIT) which is derived from quantum theory. The main advantage of this framework is that it can cater for paradoxical and irrational human decision making. Although quantum approaches for cognition have demonstrated advantages over classical probabilistic approaches and bounded rationality models, they still lack explanatory power. To address this, we introduce a novel explanatory analysis of the decision-maker's belief space. This is achieved by exploiting quantum interference effects as a way of both quantifying and explaining the decision-maker's uncertainty. We detail the main modules of the unified framework, the explanatory analysis method, and illustrate their application in situations violating the Sure Thing Principle.

The Synchronicity Principle under Quantum Probabilistic Inferences

We propose a new quantum Bayesian Network model in order to compute probabilistic inferences in decision making scenarios. The application of a quantum paradigm to decision making generates interference effects that influence probabilistic inferences. These effects do not exist in a classical setting and constitute a major issue in the decision process, because they generate quantum parameters that highly increase with the amount of uncertainty of the problem. To automatically compute these quantum parameters, we propose a heuristic inspired by Jung’s Synchronicity principle. Synchronicity can be defined by a significant coincidence that appears between a mental state and an event occurring in the external world. It is the occurrence of meaningful, but not causally connected events. We tested our quantum Bayesian Network together with the Synchronicity inspired heuristic in empirical experiments related to categorization/decision in which the law of total probability was being violated. Results showed that the proposed quantum model was able to simulate the observed empirical findings from the experiments. We then applied our model to a more general scenario and showed the differences between classical and quantum inferences in a Lung Cancer medical diagnosis Bayesian Network.

A quantum theoretical explanation for probability judgment errors

Psychological Review, 2011

A quantum probability model is introduced and used to explain human probability judgment errors including the conjunction and disjunction fallacies, averaging effects, unpacking effects, and order effects on inference. On the one hand, quantum theory is similar to other categorization and memory models of cognition in that it relies on vector spaces defined by features, and similarities between vectors to determine probability judgments. On the other hand, quantum probability theory is a generalization of Bayesian probability theory because it is based on a set of (von Neumann) axioms that relax some of the classic (Kolmogorov) axioms. The quantum model is compared and contrasted with other competing explanations for these judgment errors including the anchoring and adjustment model for probability judgments. The quantum model introduces a new fundamental concept to cognition --the compatibility versus incompatibility of questions and the effect this can have on the sequential order of judgments.

A Quantum Probability Approach to Human Causal Reasoning

PsycEXTRA Dataset

When people make inferences about causal situations with vague and imperfect information, their judgments often deviate from the normative prescription of classical probability. As a result, it is difficult to apply popular models of causal reasoning such as ∆P and causal power, which provide good accounts of behavior in casual learning tasks and tasks where statistical information is provided directly. We propose a unified explanation of human causal reasoning using quantum probability theory that can account for causal reasoning across many different domains. In our approach, we postulate a hierarchy of mental representations, from fully quantum to fully classical, that could be adopted for different situations. We illustrate our approach with new experiments and model comparisons.

Quantum cognition: a new theoretical approach to psychology

What type of probability theory best describes the way humans make judgments under uncertainty and decisions under conflict? Although rational models of cognition have become prominent and have achieved much success, they adhere to the laws of classical probability theory despite the fact that human reasoning does not always conform to these laws. For this reason we have seen the recent emergence of models based on an alternative probabilistic framework drawn from quantum theory. These quantum models show promise in addressing cognitive phenomena that have proven recalcitrant to modeling by means of classical probability theory. This review compares and contrasts probabilistic models based on Bayesian or classical versus quantum principles, and highlights the advantages and disadvantages of each approach.

Quantum Models of Cognition and Decision

Quantum Models of Cognition and Decision

Much of our understanding of human thinking is based on probabilistic models. This innovative book by Jerome R. Busemeyer and Peter D. Bruza argues that, actually, the underlying mathematical structures from quantum theory provide a much better account of human thinking than traditional models. They introduce the foundations for modelling probabilistic-dynamic systems using two aspects of quantum theory. The first, “contextuality,” is away to understand interference effects found with inferences and decisions under conditions of uncertainty. The second, “quantum entanglement,” allows cognitive phenomena to be modelled in non-reductionist ways. Employing these principles drawn from quantum theory allows us to view human cognition and decision in a totally new light. Introducing the basic principles in an easy-to-follow way, this book does not assume a physics background or a quantum brain and comes complete with a tutorial and fully worked-out applications in important areas of cognition and decision

A Quantum Probability Model of Causal Reasoning

Frontiers in Psychology, 2012

People can often outperform statistical methods and machine learning algorithms in situations that involve making inferences about the relationship between causes and effects. While people are remarkably good at causal reasoning in many situations, there are several instances where they deviate from expected responses. This paper examines three situations where judgments related to causal inference problems produce unexpected results and describes a quantum inference model based on the axiomatic principles of quantum probability theory that can explain these effects. Two of the three phenomena arise from the comparison of predictive judgments (i.e., the conditional probability of an effect given a cause) with diagnostic judgments (i.e., the conditional probability of a cause given an effect). The third phenomenon is a new finding examining order effects in predictive causal judgments. The quantum inference model uses the notion of incompatibility among different causes to account for all three phenomena. Psychologically, the model assumes that individuals adopt different points of view when thinking about different causes. The model provides good fits to the data and offers a coherent account for all three causal reasoning effects thus proving to be a viable new candidate for modeling human judgment.

Quantum Probability Explanations for Probability Judgment'Errors

2009

A quantum probability model is introduced and used to explain human probability judgment errors including the conjunction, disjunction, inverse, and conditional fallacies, as well as unpacking effects and partitioning effects. Quantum probability theory is a general and coherent theory based on a set of (von Neumann) axioms which relax some of the constraints underlying classic (Kolmogorov) probability theory. The quantum model is compared and contrasted with other competing explanations for these judgment errors including the representativeness heuristic, the averaging model, and a memory retrieval model for probability judgments. The quantum model also provides ways to extend Bayesian, fuzzy set, and fuzzy trace theories. We conclude that quantum information processing principles provide a viable and promising new way to understand human judgment and reasoning.