arXiv subjects

Sandro Sozzo

Publications and source records attributed to Sandro Sozzo.

At least 55 records · Page 3Linked to original sources

arXiv2015

From Ambiguity Aversion to a Generalized Expected Utility. Modeling Preferences in a Quantum Probabilistic Framework

Ambiguity and ambiguity aversion have been widely studied in decision theory and economics both at a theoretical and an experimental level. After Ellsberg's seminal studies challenging subjective expected utility theory (SEUT), several (mainly normative) approaches have been put forward to reproduce ambiguity aversion and Ellsberg-type preferences. However, Machina and other authors have pointed out some fundamental difficulties of these generalizations of SEUT to cope with some variants of Ellsberg's thought experiments, which has recently been experimentally confirmed. Starting from our quantum modeling approach to human cognition, we develop here a general probabilistic framework to model human decisions under uncertainty. We show that our quantum theoretical model faithfully represents different sets of data collected on both the Ellsberg and the Machina paradox situations, and is flexible enough to describe different subjective attitudes with respect to ambiguity. Our approach opens the way toward a quantum-based generalization of expected utility theory (QEUT), where subjective probabilities depend on the state of the conceptual entity at play and its interaction with the decision-maker, while preferences between acts are determined by the maximization of this 'state-dependent expected utility'.

physics.soc-ph↗

arXiv2015

Outline of a Generalization and a Reinterpretation of Quantum Mechanics Recovering Objectivity

The ESR model has been recently proposed in several papers to offer a possible solution of the problems raising from the nonobjectivity of physical properties in quantum mechanics (QM) (mainly the objectification problem of the quantum theory of measurement). This solution is obtained by embodying the mathematical formalism of QM into a broader mathematical framework and reinterpreting quantum probabilities as conditional on detection rather than absolute. We provide a new and more general formulation of the ESR model and discuss time evolution according to it, pointing out in particular that both linear and nonlinear evolution may occur, depending on the physical environment.

quant-ph↗

arXiv2015

A New Fundamental Evidence of Non-Classical Structure in the Combination of Natural Concepts

We recently performed cognitive experiments on conjunctions and negations of two concepts with the aim of investigating the combination problem of concepts. Our experiments confirmed the deviations (conceptual vagueness, underextension, overextension, etc.) from the rules of classical (fuzzy) logic and probability theory observed by several scholars in concept theory, while our data were successfully modeled in a quantum-theoretic framework developed by ourselves. In this paper, we isolate a new, very stable and systematic pattern of violation of classicality that occurs in concept combinations. In addition, the strength and regularity of this non-classical effect leads us to believe that it occurs at a more fundamental level than the deviations observed up to now. It is our opinion that we have identified a deep non-classical mechanism determining not only how concepts are combined but, rather, how they are formed. We show that this effect can be faithfully modeled in a two-sector Fock space structure, and that it can be exactly explained by assuming that human thought is the supersposition of two processes, a 'logical reasoning', guided by 'logic', and a 'conceptual reasoning' guided by 'emergence', and that the latter generally prevails over the former. All these findings provide a new fundamental support to our quantum-theoretic approach to human cognition.

cs.AI↗

arXiv2015

Quantum Structure of Negation and Conjunction in Human Thought

We analyse in this paper the data collected in a set of experiments performed on human subjects on the combination of natural concepts. We investigate the mutual influence of conceptual conjunction and negation by measuring the membership weights of a list of exemplars with respect to two concepts, e.g., 'Fruits' and 'Vegetables', and their conjunction 'Fruits And Vegetables', but also their conjunction when one or both concepts are negated, namely, 'Fruits And Not Vegetables', 'Not Fruits And Vegetables' and 'Not Fruits And Not Vegetables'. Our findings sharpen existing analysis on conceptual combinations, revealing systematic and remarkable deviations from classical (fuzzy set) logic and probability theory. And, more important, our results give further considerable evidence to the validity of our quantum-theoretic framework for the combination of two concepts. Indeed, the representation of conceptual negation naturally arises from the general assumptions of our two-sector Fock space model, and this representation faithfully agrees with the collected data. In addition, we find a further significant deviation and a priori unexpected from classicality, which can exactly be explained by assuming that human reasoning is the superposition of an 'emergent reasoning' and a 'logical reasoning', and that these two processes can be successfully represented in a Fock space algebraic structure.

cs.AI↗

arXiv2015

Quantum Structure in Cognition, Origins, Developments, Successes and Expectations

We provide an overview of the results we have attained in the last decade on the identification of quantum structures in cognition and, more specifically, in the formalization and representation of natural concepts. We firstly discuss the quantum foundational reasons that led us to investigate the mechanisms of formation and combination of concepts in human reasoning, starting from the empirically observed deviations from classical logical and probabilistic structures. We then develop our quantum-theoretic perspective in Fock space which allows successful modeling of various sets of cognitive experiments collected by different scientists, including ourselves. In addition, we formulate a unified explanatory hypothesis for the presence of quantum structures in cognitive processes, and discuss our recent discovery of further quantum aspects in concept combinations, namely, 'entanglement' and 'indistinguishability'. We finally illustrate perspectives for future research.

cs.AI↗

arXiv2014

Quantum Structure in Cognition and the Foundations of Human Reasoning

Traditional cognitive science rests on a foundation of classical logic and probability theory. This foundation has been seriously challenged by several findings in experimental psychology on human decision making. Meanwhile, the formalism of quantum theory has provided an efficient resource for modeling these classically problematical situations. In this paper, we start from our successful quantum-theoretic approach to the modeling of concept combinations to formulate a unifying explanatory hypothesis. In it, human reasoning is the superposition of two processes -- a conceptual reasoning, whose nature is emergence of new conceptuality, and a logical reasoning, founded on an algebraic calculus of the logical type. In most cognitive processes however, the former reasoning prevails over the latter. In this perspective, the observed deviations from classical logical reasoning should not be interpreted as biases but, rather, as natural expressions of emergence in its deepest form.

cs.AI↗

arXiv2014

The Quantum Nature of Identity in Human Thought: Bose-Einstein Statistics for Conceptual Indistinguishability

Increasing experimental evidence shows that humans combine concepts in a way that violates the rules of classical logic and probability theory. On the other hand, mathematical models inspired by the formalism of quantum theory are in accordance with data on concepts and their combinations. In this paper, we investigate a novel type of concept combination were a number is combined with a noun, e.g., `Eleven Animals. Our aim is to study 'conceptual identity' and the effects of 'indistinguishability' - in the combination 'Eleven Animals', the 'animals' are identical and indistinguishable - on the mechanisms of conceptual combination. We perform experiments on human subjects and find significant evidence of deviation from the predictions of classical statistical theories, more specifically deviations with respect to Maxwell-Boltzmann statistics. This deviation is of the 'same type' of the deviation of quantum mechanical from classical mechanical statistics, due to indistinguishability of microscopic quantum particles, i.e we find convincing evidence of the presence of Bose-Einstein statistics. We also present preliminary promising evidence of this phenomenon in a web-based study.

cs.AI↗

arXiv2014

A Quantum Probability Explanation in Fock Space for Borderline Contradictions

The construction of a consistent theory for structuring and representing how concepts combine and interact is one of the main challenges for the scholars involved in cognitive studies. All traditional approaches are still facing serious hindrances when dealing with combinations of concepts and concept vagueness. One of the main consequences of these difficulties is the existence of borderline cases which is hardly explainable from the point of view of classical (fuzzy set) logic and probability theory. Resting on a quantum-theoretic approach which successfully models conjunctions and disjuncions of two concepts, we propound a quantum probability model in Fock space which accords with the experimental data collected by Alxatib and Pelletier (2011) on borderline contradictions. Our model allows one to explain the occurrence of the latter contradictions in terms of genuine quantum effects, such as contextuality, superposition, interference and emergence. In particular, we claim that it is the specific mechanism of `emergence of a new concept' that is responsible of these deviations from classical logical thinking in the cognitive studies on human thought. This result seems to be compatible with a recent interesting application of quantum probabilistic modeling in the study of borderline vagueness (Blutner, Pothos & Bruza, 2012), and analogies and differences with it are sketched here.

physics.soc-ph↗

arXiv2014

Conjunction and Negation of Natural Concepts: A Quantum-theoretic Modeling

We perform two experiments with the aim to investigate the effects of negation on the combination of natural concepts. In the first experiment, we test the membership weights of a list of exemplars with respect to two concepts, e.g., {\it Fruits} and {\it Vegetables}, and their conjunction {\it Fruits And Vegetables}. In the second experiment, we test the membership weights of the same list of exemplars with respect to the same two concepts, but negating the second, e.g., {\it Fruits} and {\it Not Vegetables}, and again their conjunction {\it Fruits And Not Vegetables}. The collected data confirm existing results on conceptual combination, namely, they show dramatic deviations from the predictions of classical (fuzzy set) logic and probability theory. More precisely, they exhibit conceptual vagueness, gradeness of membership, overextension and double overextension of membership weights with respect to the given conjunctions. Then, we show that the quantum probability model in Fock space recently elaborated to model Hampton's data on concept conjunction (Hampton, 1988a) and disjunction (Hampton, 1988b) faithfully accords with the collected data. Our quantum-theoretic modeling enables to describe these non-classical effects in terms of genuine quantum effects, namely `contextuality', `superposition', `interference' and `emergence'. The obtained results confirm and strenghten the analysis in Aerts (2009a) and Sozzo (2014) on the identification of quantum aspects in experiments on conceptual vagueness. Our results can be inserted within the general research on the identification of quantum structures in cognitive and decision processes.

cs.AI↗

arXiv2014

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'.

physics.hist-ph↗

arXiv2014

Quantum Structure in Competing Lizard Communities

Almost two decades of research on applications of the mathematical formalism of quantum theory as a modeling tool in domains different from the micro-world has given rise to many successful applications in situations related to human behavior and thought, more specifically in cognitive processes of decision-making and the ways concepts are combined into sentences. In this article, we extend this approach to animal behavior, showing that an analysis of an interactive situation involving a mating competition between certain lizard morphs allows to identify a quantum theoretic structure. More in particular, we show that when this lizard competition is analyzed structurally in the light of a compound entity consisting of subentities, the contextuality provided by the presence of an underlying rock-paper-scissors cyclic dynamics leads to a violation of Bell's inequality, which means it is of a non-classical type. We work out an explicit quantum-mechanical representation in Hilbert space for the lizard situation and show that it faithfully models a set of experimental data collected on three throat-colored morphs of a specific lizard species. Furthermore, we investigate the Hilbert space modeling, and show that the states describing the lizard competitions contain entanglement for each one of the considered confrontations of lizards with different competing strategies, which renders it no longer possible to interpret these states of the competing lizards as compositions of states of the individual lizards.

physics.bio-ph↗

arXiv2014

Modeling Concept Combinations in a Quantum-theoretic Framework

We present modeling for conceptual combinations which uses the mathematical formalism of quantum theory. Our model faithfully describes a large amount of experimental data collected by different scholars on concept conjunctions and disjunctions. Furthermore, our approach sheds a new light on long standing drawbacks connected with vagueness, or fuzziness, of concepts, and puts forward a completely novel possible solution to the 'combination problem' in concept theory. Additionally, we introduce an explanation for the occurrence of quantum structures in the mechanisms and dynamics of concepts and, more generally, in cognitive and decision processes, according to which human thought is a well structured superposition of a 'logical thought' and a 'conceptual thought', and the latter usually prevails over the former, at variance with some widespread beliefs

cs.AI↗

arXiv2013

Identifying Quantum Structures in the Ellsberg Paradox

Empirical evidence has confirmed that quantum effects occur frequently also outside the microscopic domain, while quantum structures satisfactorily model various situations in several areas of science, including biological, cognitive and social processes. In this paper, we elaborate a quantum mechanical model which faithfully describes the 'Ellsberg paradox' in economics, showing that the mathematical formalism of quantum mechanics is capable to represent the 'ambiguity' present in this kind of situations, because of the presence of 'contextuality'. Then, we analyze the data collected in a concrete experiment we performed on the Ellsberg paradox and work out a complete representation of them in complex Hilbert space. We prove that the presence of quantum structure is genuine, that is, 'interference' and 'superposition' in a complex Hilbert space are really necessary to describe the conceptual situation presented by Ellsberg. Moreover, our approach sheds light on 'ambiguity laden' decision processes in economics and decision theory, and allows to deal with different Ellsberg-type generalizations, e.g., the 'Machina paradox'.

physics.soc-ph↗

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↗