arXiv subjects

Sandro Sozzo

Publications and source records attributed to Sandro Sozzo.

At least 73 records · Page 4Linked to original sources

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

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

The Quantum Harmonic Oscillator in the ESR Model

The ESR model proposes a new theoretical perspective which incorporates the mathematical formalism of standard (Hilbert space) quantum mechanics (QM) in a noncontextual framework, reinterpreting quantum probabilities as conditional on detection instead of absolute. We have provided in some previous papers mathematical representations of the physical entities introduced by the ESR model, namely observables, properties, pure states, proper and improper mixtures, together with rules for calculating conditional and overall probabilities, and for describing transformations of states induced by measurements. We study in this paper the relevant physical case of the quantum harmonic oscillator in our mathematical formalism. We reinterpret the standard quantum rules for probabilities, provide new expressions for absolute probabilities, and show how the standard state transformations must be modified according to the ESR model.

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

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

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

Extended Representations of Observables and States for a Noncontextual Reinterpretation of QM

A crucial and problematical feature of quantum mechanics (QM) is nonobjectivity of properties. The ESR model restores objectivity reinterpreting quantum probabilities as conditional on detection and embodying the mathematical formalism of QM into a broader noncontextual (hence local) framework. We propose here an improved presentation of the ESR model containing a more complete mathematical representation of the basic entities of the model. We also extend the model to mixtures showing that the mathematical representations of proper mixtures does not coincide with the mathematical representation of mixtures provided by QM, while the representation of improper mixtures does. This feature of the ESR model entails that some interpretative problems raising in QM when dealing with mixtures are avoided. From an empirical point of view the predictions of the ESR model depend on some parameters which may be such that they are very close to the predictions of QM in most cases. But the nonstandard representation of proper mixtures allows us to propose the scheme of an experiment that could check whether the predictions of QM or the predictions of the ESR model are correct.

quant-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

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↗