arXiv subjects

Diederik Aerts

Publications and source records attributed to Diederik Aerts.

At least 91 records · Page 5Linked to original sources

arXiv2013

Contextualizing concepts using a mathematical generalization of the quantum formalism

We outline the rationale and preliminary results of using the state context property (SCOP) formalism, originally developed as a generalization of quantum mechanics, to describe the contextual manner in which concepts are evoked, used and combined to generate meaning. The quantum formalism was developed to cope with problems arising in the description of (i) the measurement process, and (ii) the generation of new states with new properties when particles become entangled. Similar problems arising with concepts motivated the formal treatment introduced here. Concepts are viewed not as fixed representations, but entities existing in states of potentiality that require interaction with a context-a stimulus or another concept-to 'collapse' to an instantiated form (e.g. exemplar, prototype, or other possibly imaginary instance). The stimulus situation plays the role of the measurement in physics, acting as context that induces a change of the cognitive state from superposition state to collapsed state. The collapsed state is more likely to consist of a conjunction of concepts for associative than analytic thought because more stimulus or concept properties take part in the collapse. We provide two contextual measures of conceptual distance-one using collapse probabilities and the other weighted properties-and show how they can be applied to conjunctions using the pet fish problem.

q-bio.NC↗

arXiv2013

Intrinsic Contextuality as the Crux of Consciousness

A stream of conscious experience is extremely contextual; it is impacted by sensory stimuli, drives and emotions, and the web of associations that link, directly or indirectly, the subject of experience to other elements of the individual's worldview. The contextuality of one's conscious experience both enhances and constrains the contextuality of one's behavior. Since we cannot know first-hand the conscious experience of another, it is by way of behavioral contextuality that we make judgements about whether or not, and to what extent, a system is conscious. Thus we believe that a deep understanding of contextuality is vital to the study of consciousness. Methods have been developed for handling contextuality in the microworld of quantum particles. Our goal has been to investigate the extent to which these methods can be used to analyze contextuality in conscious experience. This work is the fledgling efforts of a recently-initiated interdisciplinary collaboration.

q-bio.NC↗

arXiv2013

Toward a Formal Model of the Shifting Relationship between Concepts and Contexts during Associative Thought

The quantum inspired State Context Property (SCOP) theory of concepts is unique amongst theories of concepts in offering a means of incorporating that for each concept in each different context there are an unlimited number of exemplars, or states, of varying degrees of typicality. Working with data from a study in which participants were asked to rate the typicality of exemplars of a concept for different contexts, and introducing an exemplar typicality threshold, we built a SCOP model of how states of a concept arise differently in associative versus analytic (or divergent and convergent) modes of thought. Introducing measures of state robustness and context relevance, we show that by varying the threshold, the relevance of different contexts changes, and seemingly atypical states can become typical. The formalism provides a pivotal step toward a formal explanation of creative thought proesses.

q-bio.NC↗

arXiv2013

Quantum Structure in Cognition: Why and How Concepts are Entangled

One of us has recently elaborated a theory for modelling concepts that uses the state context property (SCoP) formalism, i.e. a generalization of the quantum formalism. This formalism incorporates context into the mathematical structure used to represent a concept, and thereby models how context influences the typicality of a single exemplar and the applicability of a single property of a concept, which provides a solution of the 'Pet-Fish problem' and other difficulties occurring in concept theory. Then, a quantum model has been worked out which reproduces the membership weights of several exemplars of concepts and their combinations. We show in this paper that a further relevant effect appears in a natural way whenever two or more concepts combine, namely, 'entanglement'. The presence of entanglement is explicitly revealed by considering a specific example with two concepts, constructing some Bell's inequalities for this example, testing them in a real experiment with test subjects, and finally proving that Bell's inequalities are violated in this case. We show that the intrinsic and unavoidable character of entanglement can be explained in terms of the weights of the exemplars of the combined concept with respect to the weights of the exemplars of the component concepts.

physics.soc-ph↗

arXiv2013

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.

cs.AI↗

arXiv2013

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.

cs.AI↗

arXiv2013

Quantum Entanglement in Concept Combinations

Research in the application of quantum structures to cognitive science confirms that these structures quite systematically appear in the dynamics of concepts and their combinations and quantum-based models faithfully represent experimental data of situations where classical approaches are problematical. In this paper, we analyze the data we collected in an experiment on a specific conceptual combination, showing that Bell's inequalities are violated in the experiment. We present a new refined entanglement scheme to model these data within standard quantum theory rules, where 'entangled measurements and entangled evolutions' occur, in addition to the expected 'entangled states', and present a full quantum representation in complex Hilbert space of the data. This stronger form of entanglement in measurements and evolutions might have relevant applications in the foundations of quantum theory, as well as in the interpretation of nonlocality tests. It could indeed explain some non-negligible 'anomalies' identified in EPR-Bell experiments.

cs.AI↗

arXiv2013

Systems, environments, and soliton rate equations: A non-Kolmogorovian framework for population dynamics

Soliton rate equations are based on non-Kolmogorovian models of probability and naturally include autocatalytic processes. The formalism is not widely known but has great unexplored potential for applications to systems interacting with environments. Beginning with links of contextuality to non-Kolmogorovity we introduce the general formalism of soliton rate equations and work out explicit examples of subsystems interacting with environments. Of particular interest is the case of a soliton autocatalytic rate equation coupled to a linear conservative environment, a formal way of expressing seasonal changes. Depending on strength of the system-environment coupling we observe phenomena analogous to hibernation or even complete blocking of decay of a population.

q-bio.PE↗

arXiv2013

The Quantum Challenge in Concept Theory and Natural Language Processing

The mathematical formalism of quantum theory has been successfully used in human cognition to model decision processes and to deliver representations of human knowledge. As such, quantum cognition inspired tools have improved technologies for Natural Language Processing and Information Retrieval. In this paper, we overview the quantum cognition approach developed in our Brussels team during the last two decades, specifically our identification of quantum structures in human concepts and language, and the modeling of data from psychological and corpus-text-based experiments. We discuss our quantum-theoretic framework for concepts and their conjunctions/disjunctions in a Fock-Hilbert space structure, adequately modeling a large amount of data collected on concept combinations. Inspired by this modeling, we put forward elements for a quantum contextual and meaning-based approach to information technologies in which 'entities of meaning' are inversely reconstructed from texts, which are considered as traces of these entities' states.

cs.CL↗

arXiv2013

Quantum and Concept Combination, Entangled Measurements and Prototype Theory

We analyze the meaning of the violation of the marginal probability law for situations of correlation measurements where entanglement is identified. We show that for quantum theory applied to the cognitive realm such a violation does not lead to the type of problems commonly believed to occur in situations of quantum theory applied to the physical realm. We briefly situate our quantum approach for modeling concepts and their combinations with respect to the notions of 'extension' and 'intension' in theories of meaning, and in existing concept theories.

cs.AI↗

arXiv2013

General Quantum Hilbert Space Modeling Scheme for Entanglement

We work out a classification scheme for quantum modeling in Hilbert space of any kind of composite entity violating Bell's inequalities and exhibiting entanglement. Our theoretical framework includes situations with entangled states and product measurements ('customary quantum situation'), and also situations with both entangled states and entangled measurements ('nonlocal box situation', 'nonlocal non-marginal box situation'). We show that entanglement is structurally a joint property of states and measurements. Furthermore, entangled measurements enable quantum modeling of situations that are usually believed to be 'beyond quantum'. Our results are also extended from pure states to quantum mixtures.

quant-ph↗

arXiv2013

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.

cs.IR↗

arXiv2013

Concepts and Their Dynamics: A Quantum-Theoretic Modeling of Human Thought

We analyze different aspects of our quantum modeling approach of human concepts, and more specifically focus on the quantum effects of contextuality, interference, entanglement and emergence, illustrating how each of them makes its appearance in specific situations of the dynamics of human concepts and their combinations. We point out the relation of our approach, which is based on an ontology of a concept as an entity in a state changing under influence of a context, with the main traditional concept theories, i.e. prototype theory, exemplar theory and theory theory. We ponder about the question why quantum theory performs so well in its modeling of human concepts, and shed light on this question by analyzing the role of complex amplitudes, showing how they allow to describe interference in the statistics of measurement outcomes, while in the traditional theories statistics of outcomes originates in classical probability weights, without the possibility of interference. The relevance of complex numbers, the appearance of entanglement, and the role of Fock space in explaining contextual emergence, all as unique features of the quantum modeling, are explicitly revealed in this paper by analyzing human concepts and their dynamics.

cs.AI↗

arXiv2013

Quantum Structure in Economics: The Ellsberg Paradox

The 'expected utility hypothesis' and 'Savage's Sure-Thing Principle' are violated in real life decisions, as shown by the 'Allais' and 'Ellsberg paradoxes'. The popular explanation in terms of 'ambiguity aversion' is not completely accepted. As a consequence, uncertainty is still problematical in economics. To overcome these difficulties a distinction between 'risk' and 'ambiguity' has been introduced which depends on the existence of a Kolmogorovian probabilistic structure modeling these uncertainties. 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 framework admitting a quantum-like representation. For this reason, we have recently introduced a notion of 'contextual risk' to mathematically capture situations in which ambiguity occurs. 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', and conceptually supports the thesis of several authors suggesting the presence of quantum structure in economics and decision theory.

physics.soc-ph↗

arXiv2012

Potentiality States: Quantum versus Classical Emergence

We identify emergence with the existence of states of potentiality related to relevant physical quantities. We introduce the concept of 'potentiality state' operationally and show how it reduces to 'superposition state' when standard quantum mechanics can be applied. We consider several examples to illustrate our approach, and define the potentiality states giving rise to emergence in each example. We prove that Bell inequalities are violated by the potentiality states in the examples, which, taking into account Pitowsky's theorem, experimentally indicates the presence of quantum structure in emergence. In the first example emergence arises because of the many ways water can be subdivided into different vessels. In the second example, we put forward a full quantum description of the Liar paradox situation, and identify the potentiality states, which in this case turn out to be superposition states. In the example of the soccer team, we show the difference between classical emergence as stable dynamical pattern and emergence defined by a potentiality state, and show how Bell inequalities can be violated in the case of highly contextual experiments.

quant-ph↗

arXiv2012

On the Foundations of the Theory of Evolution

Darwinism conceives evolution as a consequence of random variation and natural selection, hence it is based on a materialistic, i.e. matter-based, view of science inspired by classical physics. But matter in itself is considered a very complex notion in modern physics. More specifically, at a microscopic level, matter and energy are no longer retained within their simple form, and quantum mechanical models are proposed wherein potential form is considered in addition to actual form. In this paper we propose an alternative to standard Neodarwinian evolution theory. We suggest that the starting point of evolution theory cannot be limited to actual variation whereupon is selected, but to variation in the potential of entities according to the context. We therefore develop a formalism, referred to as Context driven Actualization of Potential (CAP), which handles potentiality and describes the evolution of entities as an actualization of potential through a reiterated interaction with the context. As in quantum mechanics, lack of knowledge of the entity, its context, or the interaction between context and entity leads to different forms of indeterminism in relation to the state of the entity. This indeterminism generates a non-Kolmogorovian distribution of probabilities that is different from the classical distribution of chance described by Darwinian evolution theory, which stems from a 'actuality focused', i.e. materialistic, view of nature. We also present a quantum evolution game that highlights the main differences arising from our new perspective and shows that it is more fundamental to consider evolution in general, and biological evolution in specific, as a process of actualization of potential induced by context, for which its material reduction is only a special case.

physics.bio-ph↗

arXiv2012

Quantum Model Theory (QMod): Modeling Contextual Emergent Entangled Interfering Entities

In this paper we present 'Quantum Model Theory' (QMod), a theory we developed to model entities that entail the typical quantum effects of 'contextuality', 'superposition', 'interference', 'entanglement' and 'emergence'. The aim of QMod is to put forward a theoretical framework that is more general than standard quantum mechanics, in the sense that, for its complex version it only uses this quantum calculus locally, i.e. for each context corresponding to a measurement, and for its real version it does not need the property of 'linearity of the set of states' to model the quantum effect. In this sense, QMod is a generalization of quantum mechanics, similar to how the general relativity manifold mathematical formalism is a generalization of special relativity. We prove by means of a representation theorem that QMod can be used for any entity entailing the typical quantum effects mentioned above. Some examples of application of QMod in concept theory and macroscopic physics are also considered.

math-ph↗

arXiv2012

The Guppy Effect as Interference

People use conjunctions and disjunctions of concepts in ways that violate the rules of classical logic, such as the law of compositionality. Specifically, they overextend conjunctions of concepts, a phenomenon referred to as the Guppy Effect. We build on previous efforts to develop a quantum model that explains the Guppy Effect in terms of interference. Using a well-studied data set with 16 exemplars that exhibit the Guppy Effect, we developed a 17-dimensional complex Hilbert space H that models the data and demonstrates the relationship between overextension and interference. We view the interference effect as, not a logical fallacy on the conjunction, but a signal that out of the two constituent concepts, a new concept has emerged.

cs.AI↗