arXiv subjects

Diederik Aerts

Publications and source records attributed to Diederik Aerts.

At least 109 records · Page 6Linked to original sources

arXiv2012

A Quantum Model for the Ellsberg and Machina Paradoxes

The Ellsberg and Machina paradoxes reveal that expected utility theory is problematical when real subjects take decisions under uncertainty. Suitable generalizations of expected utility exist which attempt to solve the Ellsberg paradox, but none of them provides a satisfactory solution of the Machina paradox. In this paper we elaborate a quantum model in Hilbert space describing the Ellsberg situation and also the Machina situation, and show that we can model the specific aspect of the Machina situation that is unable to be modeled within the existing generalizations of expected utility.

physics.soc-ph↗

arXiv2012

Quantum Interference in Cognition: Structural Aspects of the Brain

We identify the presence of typically quantum effects, namely 'superposition' and 'interference', in what happens when human concepts are combined, and provide a quantum model in complex Hilbert space that represents faithfully experimental data measuring the situation of combining concepts. Our model shows how 'interference of concepts' explains the effects of underextension and overextension when two concepts combine to the disjunction of these two concepts. This result supports our earlier hypothesis that human thought has a superposed two-layered structure, one layer consisting of 'classical logical thought' and a superposed layer consisting of 'quantum conceptual thought'. Possible connections with recent findings of a 'grid-structure' for the brain are analyzed, and influences on the mind/brain relation, and consequences on applied disciplines, such as artificial intelligence and quantum computation, are considered.

cs.AI↗

arXiv2012

Entanglement of Conceptual Entities in Quantum Model Theory (QMod)

We have recently elaborated 'Quantum Model Theory' (QMod) to model situations where the quantum effects of contextuality, interference, superposition, entanglement and emergence, appear without the entities giving rise to these situations having necessarily to be of microscopic nature. We have shown that QMod models without introducing linearity for the set of the states. In this paper we prove that QMod, although not using linearity for the state space, provides a method of identification for entangled states and an intuitive explanation for their occurrence. We illustrate this method for entanglement identification with concrete examples.

math-ph↗

arXiv2011

A Quantum-like Approach to the Stock Market

Modern approaches to stock pricing in quantitative finance are typically founded on the 'Black-Scholes model' and the underlying 'random walk hypothesis'. Empirical data indicate that this hypothesis works well in stable situations but, in abrupt transitions such as during an economical crisis, the random walk model fails and alternative descriptions are needed. For this reason, several proposals have been recently forwarded which are based on the formalism of quantum mechanics. In this paper we apply the 'SCoP formalism', elaborated to provide an operational foundation of quantum mechanics, to the stock market. We argue that a stock market is an intrinsically contextual system where agents' decisions globally influence the market system and stocks prices, determining a nonclassical behavior. More specifically, we maintain that a given stock does not generally have a definite value, e.g., a price, but its value is actualized as a consequence of the contextual interactions in the trading process. This contextual influence is responsible of the non-Kolmogorovian quantum-like behavior of the market at a statistical level. Then, we propose a 'sphere model' within our 'hidden measurement formalism' that describes a buying/selling process of a stock and shows that it is intuitively reasonable to assume that the stock has not a definite price until it is traded. This result is relevant in our opinion since it provides a theoretical support to the use of quantum models in finance.

q-fin.GN↗

arXiv2011

Quantum Theory and Conceptuality: Matter, Stories, Semantics and Space-Time

We elaborate the new interpretation of quantum theory that we recently proposed, according to which quantum particles are considered conceptual entities mediating between pieces of ordinary matter which are considered to act as memory structures for them. Our aim is to identify what is the equivalent for the human cognitive realm of what physical space-time is for the realm of quantum particles and ordinary matter. For this purpose, we identify the notion of 'story' as the equivalent within the human cognitive realm of what ordinary matter is in the physical quantum realm, and analyze the role played by the logical connectives of disjunction and conjunction with respect to the notion of locality. Similarly to what we have done in earlier investigations on this new quantum interpretation, we use the specific cognitive environment of the World-Wide Web to elucidate the comparisons we make between the human cognitive realm and the physical quantum realm.

quant-ph↗

arXiv2011

Quantum Axiomatics: Topological and Classical Properties of State Property Systems

The definition of 'classical state', and how it was used in earlier work to prove a decomposition theorem internally in the language of State Property Systems, presupposes as an additional datum an orthocomplementation on the property lattice of a physical system. In this paper we argue on the basis of the epsilon-model on the Poincare sphere that a notion of 'topologicity' for states can be seen as an alternative (operationally foundable) classicality notion in the absence of an orthocomplementation, and compare it to the known and operationally founded concept of classicality.

quant-ph↗

arXiv2011

Contextual Risk and Its Relevance in Economics

Uncertainty in economics still poses some fundamental problems illustrated, e.g., by the Allais and Ellsberg paradoxes. To overcome these difficulties, economists have introduced an interesting distinction between 'risk' and 'ambiguity' depending on the existence of a (classical Kolmogorovian) probabilistic structure modeling these uncertainty situations. On the other hand, evidence of everyday life suggests that 'context' plays a fundamental role in human decisions under uncertainty. Moreover, it is well known from physics that any probabilistic structure modeling contextual interactions between entities structurally needs a non-Kolmogorovian quantum-like framework. In this paper we introduce the notion of 'contextual risk' with the aim of modeling a substantial part of the situations in which usually only 'ambiguity' is present. More precisely, we firstly introduce the essentials of an operational formalism called 'the hidden measurement approach' in which probability is introduced as a consequence of fluctuations in the interaction between entities and contexts. Within the hidden measurement approach we propose a 'sphere model' as a mathematical tool for situations in which contextual risk occurs. We show that a probabilistic model of this kind is necessarily non-Kolmogorovian, hence it requires either the formalism of quantum mechanics or a generalization of it. This insight is relevant, for it explains the presence of quantum or, better, quantum-like, structures in economics, as suggested by some authors, and can serve to solve the aforementioned paradoxes.

physics.soc-ph↗

arXiv2011

A Contextual Risk Model for the Ellsberg Paradox

The Allais and Ellsberg paradoxes show that the expected utility hypothesis and Savage's Sure-Thing Principle are violated in real life decisions. The popular explanation in terms of 'ambiguity aversion' is not completely accepted. On the other hand, we have recently introduced a notion of 'contextual risk' to mathematically capture what is known as 'ambiguity' in the economics literature. Situations in which contextual risk occurs cannot be modeled by Kolmogorovian classical probabilistic structures, but a non-Kolmogorovian framework with a quantum-like structure is needed. We prove in this paper that the contextual risk approach can be applied to the Ellsberg paradox, and elaborate a 'sphere model' within our 'hidden measurement formalism' which reveals that it is the overall conceptual landscape that is responsible of the disagreement between actual human decisions and the predictions of expected utility theory, which generates the paradox. This result points to the presence of a 'quantum conceptual layer' in human thought which is superposed to the usually assumed 'classical logical layer'.

physics.soc-ph↗

arXiv2011

Quantum Structure in Cognition: Fundamentals and Applications

Experiments in cognitive science and decision theory show that the ways in which people combine concepts and make decisions cannot be described by classical logic and probability theory. This has serious implications for applied disciplines such as information retrieval, artificial intelligence and robotics. Inspired by a mathematical formalism that generalizes quantum mechanics the authors have constructed a contextual framework for both concept representation and decision making, together with quantum models that are in strong alignment with experimental data. The results can be interpreted by assuming the existence in human thought of a double-layered structure, a 'classical logical thought' and a 'quantum conceptual thought', the latter being responsible of the above paradoxes and nonclassical effects. The presence of a quantum structure in cognition is relevant, for it shows that quantum mechanics provides not only a useful modeling tool for experimental data but also supplies a structural model for human and artificial thought processes. This approach has strong connections with theories formalizing meaning, such as semantic analysis, and has also a deep impact on computer science, information retrieval and artificial intelligence. More specifically, the links with information retrieval are discussed in this paper.

cs.AI↗

arXiv2011

Quantum Interaction Approach in Cognition, Artificial Intelligence and Robotics

The mathematical formalism of quantum mechanics has been successfully employed in the last years to model situations in which the use of classical structures gives rise to problematical situations, and where typically quantum effects, such as 'contextuality' and 'entanglement', have been recognized. This 'Quantum Interaction Approach' is briefly reviewed in this paper focusing, in particular, on the quantum models that have been elaborated to describe how concepts combine in cognitive science, and on the ensuing identification of a quantum structure in human thought. We point out that these results provide interesting insights toward the development of a unified theory for meaning and knowledge formalization and representation. Then, we analyze the technological aspects and implications of our approach, and a particular attention is devoted to the connections with symbolic artificial intelligence, quantum computation and robotics.

cs.AI↗

arXiv2011

A Quantum Cognition Analysis of the Ellsberg Paradox

The 'expected utility hypothesis' is one of the foundations of classical approaches to economics and decision theory and Savage's 'Sure-Thing Principle' is a fundamental element of it. It has been put forward that real-life situations exist, illustrated by the 'Allais' and 'Ellsberg paradoxes', in which the Sure-Thing Principle is violated, and where also the expected utility hypothesis does not hold. We have recently presented strong arguments for the presence of a double layer structure, a 'classical logical' and a 'quantum conceptual', in human thought and that the quantum conceptual mode is responsible of the above violation. We consider in this paper the Ellsberg paradox, perform an experiment with real test subjects on the situation considered by Ellsberg, and use the collected data to elaborate a model for the conceptual landscape surrounding the decision situation of the paradox. We show that it is the conceptual landscape which gives rise to a violation of the Sure-Thing Principle and leads to the paradoxical situation discovered by Ellsberg.

physics.soc-ph↗

arXiv2011

A Quantum-Conceptual Explanation of Violations of Expected Utility in Economics

The expected utility hypothesis is one of the building blocks of classical economic theory and founded on Savage's Sure-Thing Principle. It has been put forward, e.g. by situations such as the Allais and Ellsberg paradoxes, that real-life situations can violate Savage's Sure-Thing Principle and hence also expected utility. We analyze how this violation is connected to the presence of the 'disjunction effect' of decision theory and use our earlier study of this effect in concept theory to put forward an explanation of the violation of Savage's Sure-Thing Principle, namely the presence of 'quantum conceptual thought' next to 'classical logical thought' within a double layer structure of human thought during the decision process. Quantum conceptual thought can be modeled mathematically by the quantum mechanical formalism, which we illustrate by modeling the Hawaii problem situation, a well-known example of the disjunction effect, and we show how the dynamics in the Hawaii problem situation is generated by the whole conceptual landscape surrounding the decision situation.

physics.soc-ph↗

arXiv2010

The Pet-Fish problem on the World-Wide Web

We identify the presence of Pet-Fish problem situations and the corresponding Guppy effect of concept theory on the World-Wide Web. For this purpose, we introduce absolute weights for words expressing concepts and relative weights between words expressing concepts, and the notion of 'meaning bound' between two words expressing concepts, making explicit use of the conceptual structure of the World-Wide Web. The Pet-Fish problem occurs whenever there are exemplars - in the case of Pet and Fish these can be Guppy or Goldfish - for which the meaning bound with respect to the conjunction is stronger than the meaning bounds with respect to the individual concepts.

cs.AI↗

arXiv2010

Measuring Meaning on the World-Wide Web

We introduce the notion of the 'meaning bound' of a word with respect to another word by making use of the World-Wide Web as a conceptual environment for meaning. The meaning of a word with respect to another word is established by multiplying the product of the number of webpages containing both words by the total number of webpages of the World-Wide Web, and dividing the result by the product of the number of webpages for each of the single words. We calculate the meaning bounds for several words and analyze different aspects of these by looking at specific examples.

cs.AI↗

arXiv2010

A Potentiality and Conceptuality Interpretation of Quantum Physics

We elaborate on a new interpretation of quantum mechanics which we introduced recently. The main hypothesis of this new interpretation is that quantum particles are entities interacting with matter conceptually, which means that pieces of matter function as interfaces for the conceptual content carried by the quantum particles. We explain how our interpretation was inspired by our earlier analysis of non-locality as non-spatiality and a specific interpretation of quantum potentiality, which we illustrate by means of the example of two interconnected vessels of water. We show by means of this example that philosophical realism is not in contradiction with the recent findings with respect to Leggett's inequalities and their violations. We explain our recent work on using the quantum formalism to model human concepts and their combinations and how this has given rise to the foundational ideas of our new quantum interpretation. We analyze the equivalence of meaning in the realm of human concepts and coherence in the realm of quantum particles, and how the duality of abstract and concrete leads naturally to a Heisenberg uncertainty relation. We illustrate the role played by interference and entanglement and show how the new interpretation explains the problems related to identity and individuality in quantum mechanics. We put forward a possible scenario for the emergence of the reality of macroscopic objects.

quant-ph↗

arXiv2010

Quantum Interference and Superposition in Cognition: Development of a Theory for the Disjunction of Concepts

We elaborate a theory for the modeling of concepts using the mathematical structure of quantum mechanics. Concepts are represented by vectors in the complex Hilbert space of quantum mechanics and membership weights of items are modeled by quantum weights calculated following the quantum rules. We apply this theory to model the disjunction of concepts and show that experimental data of membership weights of items with respect to the disjunction of concepts can be modeled accurately. It is the quantum effects of interference and superposition, combined with an effect of context, that are at the origin of the effects of overextension and underextension observed as deviations from a classical use of the disjunction. We put forward a graphical explanation of the effects of overextension and underextension by interpreting the quantum model applied to the modeling of the disjunction of concepts.

physics.gen-ph↗

arXiv2010

Quantum Particles as Conceptual Entities: A Possible Explanatory Framework for Quantum Theory

We put forward a possible new interpretation and explanatory framework for quantum theory. The basic hypothesis underlying this new framework is that quantum particles are conceptual entities. More concretely, we propose that quantum particles interact with ordinary matter, nuclei, atoms, molecules, macroscopic material entities, measuring apparatuses, ..., in a similar way to how human concepts interact with memory structures, human minds or artificial memories. We analyze the most characteristic aspects of quantum theory, i.e. entanglement and non-locality, interference and superposition, identity and individuality in the light of this new interpretation, and we put forward a specific explanation and understanding of these aspects. The basic hypothesis of our framework gives rise in a natural way to a Heisenberg uncertainty principle which introduces an understanding of the general situation of 'the one and the many' in quantum physics. A specific view on macro and micro different from the common one follows from the basic hypothesis and leads to an analysis of Schrodinger's Cat paradox and the measurement problem different from the existing ones. We reflect about the influence of this new quantum interpretation and explanatory framework on the global nature and evolutionary aspects of the world and human worldviews, and point out potential explanations for specific situations, such as the generation problem in particle physics, the confinement of quarks and the existence of dark matter.

quant-ph↗

arXiv2010

Interpreting Quantum Particles as Conceptual Entities

We elaborate an interpretation of quantum physics founded on the hypothesis that quantum particles are conceptual entities playing the role of communication vehicles between material entities composed of ordinary matter which function as memory structures for these quantum particles. We show in which way this new interpretation gives rise to a natural explanation for the quantum effects of interference and entanglement by analyzing how interference and entanglement emerge for the case of human concepts. We put forward a scheme to derive a metric based on similarity as a predecessor for the structure of 'space, time, momentum, energy' and 'quantum particles interacting with ordinary matter' underlying standard quantum physics, within the new interpretation, and making use of aspects of traditional quantum axiomatics. More specifically, we analyze how the effect of non-locality arises as a consequence of the confrontation of such an emerging metric type of structure and the remaining presence of the basic conceptual structure on the fundamental level, with the potential of being revealed in specific situations.

quant-ph↗