209 research outputs found
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Zeno’s paradox in decision making
Classical probability theory has been influential in modeling decision processes, despite empirical findings that have been persistently paradoxical from classical perspectives. For such findings, some researchers have been successfully pursuing decision models based on quantum theory. One unique feature of quantum theory is the collapse postulate, which entails that measurements (or in decision making, judgments) reset the state to be consistent with the measured outcome. If there is quantum structure in cognition, then there has to be evidence for the collapse postulate. A striking, a priori prediction, is that opinion change will be slowed down (under idealized conditions frozen) by continuous judgments. In physics, this is the quantum Zeno effect. We demonstrate a quantum Zeno effect in decision making in humans and so provide evidence that advocates the use of quantum principles in decision theory, at least in some cases
Entanglement Zoo II: Examples in Physics and Cognition
We have recently presented a general scheme enabling quantum modeling of
different types of situations that violate Bell's inequalities. In this paper,
we specify this scheme for a combination of two concepts. We work out a quantum
Hilbert space model where 'entangled measurements' occur in addition to the
expected 'entanglement between the component concepts', or 'state
entanglement'. We extend this result to a macroscopic physical entity, the
'connected vessels of water', which maximally violates Bell's inequalities. We
enlighten the structural and conceptual analogies between the cognitive and
physical situations which are both examples of a nonlocal non-marginal box
modeling in our classification.Comment: 11 page
Eigenlogic: a Quantum View for Multiple-Valued and Fuzzy Systems
We propose a matrix model for two- and many-valued logic using families of
observables in Hilbert space, the eigenvalues give the truth values of logical
propositions where the atomic input proposition cases are represented by the
respective eigenvectors. For binary logic using the truth values {0,1} logical
observables are pairwise commuting projectors. For the truth values {+1,-1} the
operator system is formally equivalent to that of a composite spin 1/2 system,
the logical observables being isometries belonging to the Pauli group. Also in
this approach fuzzy logic arises naturally when considering non-eigenvectors.
The fuzzy membership function is obtained by the quantum mean value of the
logical projector observable and turns out to be a probability measure in
agreement with recent quantum cognition models. The analogy of many-valued
logic with quantum angular momentum is then established. Logical observables
for three-value logic are formulated as functions of the Lz observable of the
orbital angular momentum l=1. The representative 3-valued 2-argument logical
observables for the Min and Max connectives are explicitly obtained.Comment: 11 pages, 2 table
Meaning-focused and Quantum-inspired Information Retrieval
In recent years, quantum-based methods have promisingly integrated the
traditional procedures in information retrieval (IR) and natural language
processing (NLP). Inspired by our research on the identification and
application of quantum structures in cognition, more specifically our work on
the representation of concepts and their combinations, we put forward a
'quantum meaning based' framework for structured query retrieval in text
corpora and standardized testing corpora. This scheme for IR rests on
considering as basic notions, (i) 'entities of meaning', e.g., concepts and
their combinations and (ii) traces of such entities of meaning, which is how
documents are considered in this approach. The meaning content of these
'entities of meaning' is reconstructed by solving an 'inverse problem' in the
quantum formalism, consisting of reconstructing the full states of the entities
of meaning from their collapsed states identified as traces in relevant
documents. The advantages with respect to traditional approaches, such as
Latent Semantic Analysis (LSA), are discussed by means of concrete examples.Comment: 11 page
Do preferences and beliefs in dilemma games exhibit complementarity?
Blanco et. al. (2014) show in a novel experiment the presence of intrinsic interactions between the preferences and the beliefs of participants in social dilemma games. They discuss the identification of three effects, and we claim that two of them are inherently of non-classical nature. Here, we discuss qualitatively how a model based on complementarity between preferences and beliefs in a Hilbert space can give an structural explanation to two of the three effects the authors observe, and the third one can be incorporated into the model as a classical correlation between the observations in two subspaces. Quantitative formalization of the model and proper fit to the experimental observation will be done in the near future, as we have been given recent access to the original dataset
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An investigation of a quantum probability model for the constructive effect of affective evaluation
The idea that choices can have a constructive effect has received a great deal of empirical support. The act of choosing appears to influence subsequent preferences for the options available. Recent research has proposed a cognitive model based on quantum probability, which suggests that whether or not a participant provides an affective evaluation for a positively or negatively valenced stimulus can also be constructive and so e.g. influence the affective evaluation of a second oppositely valenced stimulus. However, there are some outstanding methodological questions in relation to this previous research. This paper reports the results of three experiments designed to resolve these questions. Experiment 1, using a binary response format, provides partial support for the interaction predicted by the quantum probability model and Experiment 2, which controls for the length of time participants have to respond, fully supports the quantum probability model. Finally, Experiment 3 sought to determine whether the key effect can generalize beyond affective judgements about visual stimuli. Using judgements about the trustworthiness of well-known people, the predictions of the quantum probability model were confirmed. Together these three experiments provide further support for the quantum probability model of the constructive effect of simple evaluations
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Towards a quantum probability theory of similarity judgments
We review recent progress in understanding similarity judgments in cognition by means of quantum probability theory (QP) models. We begin by outlining some features of similarity judgments that have proven difficult to model by traditional approaches. We then briefly present a model of similarity judgments based on QP, and show how it can solve many of the problems faced by traditional approaches. Finally we look at some areas where the quantum model is currently less satisfactory, and discuss some open questions and areas for further work
Entanglement Zoo I: Foundational and Structural Aspects
We put forward a general classification for a structural description of the
entanglement present in compound entities experimentally violating Bell's
inequalities, making use of a new entanglement scheme that we developed
recently. Our scheme, although different from the traditional one, is
completely compatible with standard quantum theory, and enables quantum
modeling in complex Hilbert space for different types of situations. Namely,
situations where entangled states and product measurements appear ('customary
quantum modeling'), and situations where states and measurements and evolutions
between measurements are entangled ('nonlocal box modeling', 'nonlocal
non-marginal box modeling'). The role played by Tsirelson's bound and marginal
distribution law is emphasized. Specific quantum models are worked out in
detail in complex Hilbert space within this new entanglement scheme.Comment: 11 page
What is Quantum? Unifying Its Micro-Physical and Structural Appearance
We can recognize two modes in which 'quantum appears' in macro domains: (i) a
'micro-physical appearance', where quantum laws are assumed to be universal and
they are transferred from the micro to the macro level if suitable 'quantum
coherence' conditions (e.g., very low temperatures) are realized, (ii) a
'structural appearance', where no hypothesis is made on the validity of quantum
laws at a micro level, while genuine quantum aspects are detected at a
structural-modeling level. In this paper, we inquire into the connections
between the two appearances. We put forward the explanatory hypothesis that,
'the appearance of quantum in both cases' is due to 'the existence of a
specific form of organisation, which has the capacity to cope with random
perturbations that would destroy this organisation when not coped with'. We
analyse how 'organisation of matter', 'organisation of life', and 'organisation
of culture', play this role each in their specific domain of application, point
out the importance of evolution in this respect, and put forward how our
analysis sheds new light on 'what quantum is'.Comment: 10 page
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Towards an empirical test of realism in cognition
We review recent progress in designing an empirical test of (temporal) realism in cognition. Realism in this context is the property that cognitive variables always have well defined (if possibly unknown) values at all times. We focus most of our attention in this contribution on discussing the exact notion of realism that is to be tested, as we feel this issue has not received enough attention to date. We also give a brief outline of the empirical test, including some comments on an experimental realisation, and we discuss what we should conclude from any purported experimental ‘disproof’ of realism. This contribution is based on Yearsley and Pothos (2014)
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