Tomas Veloz

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 modelled 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 modelled in a two-sector Fock space structure, and that it can be exactly explained by assuming that human thought is the superposition 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 new fundamental support to our quantum-theoretic approach to human cognition.

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.

Quantum Structure of Negation and Conjunction in Human Thought

We analyze in this paper the data collected in a set of experiments investigating how people combine natural concepts. We study 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 and advance existing analysis on conceptual combinations, revealing systematic 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 new significant and a priori unexpected deviation 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 are represented in a Fock space algebraic structure.

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 [1,2,3], 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

Reaction networks and evolutionary game theory

{\cal H}

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

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.

Toward a formal model of the shifting relationship between concepts and contexts during associative thought

The powerful mathematical tools developed for the study of large scale reaction networks have given rise to applications of this framework beyond the scope of biochemistry. Recently, reaction networks have been suggested as an alternative way to model social phenomena. In this “socio-chemical metaphor” molecular species play the role of agents’ decisions and their outcomes, and chemical reactions play the role of interactions among these decisions. From here, it is possible to study the dynamical properties of social systems using standard tools of biochemical modelling. In this work we show how to use reaction networks to model systems that are usually studied via evolutionary game theory. We first illustrate our framework by modeling the repeated prisoners’ dilemma. The model is built from the payoff matrix together with assumptions of the agents’ memory and recognizability capacities. The model provides consistent results concerning the performance of the agents, and allows for the examination of the steady states of the system in a simple manner. We further develop a model considering the interaction among Tit for Tat and Defector agents. We produce analytical results concerning the performance of the strategies in different situations of agents’ memory and recognizability. This approach unites two important theories and may produce new insights in classical problems such as the evolution of cooperation in large scale systems.

Context and interference effects in the combinations of natural concepts

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 new connection between concepts and quantum entities, namely the way both behave with respect to ‘identity’ and ‘indistinguishability’. We do this by considering conceptual entities of the type Eleven Animals, were a number is combined with a noun. In the combination Eleven Animals, indeed the ‘animals’ are identical and indistinguishable, and our investigation aims at identifying the nature of this conceptual identity and indistinguishability. 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.

Testing Quantum Models of Conjunction Fallacy on the World Wide Web

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 a state-transition 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 expected typicality for both states and contexts, we show that by varying the threshold, the expected typicality of different contexts changes, and seemingly atypical states can become typical. The formalism provides a pivotal step toward a formal explanation of creative thought processes.

Quantum Cognition Beyond Hilbert Space: Fundamentals and Applications

The mathematical formalism of quantum theory exhibits significant effectiveness when applied to cognitive phenomena that have resisted traditional (set theoretical) modeling. Relying on a decade of research on the operational foundations of micro-physical and conceptual entities, we present a theoretical framework for the representation of concepts and their conjunctions and disjunctions that uses the quantum formalism. This framework provides a unified solution to the ‘conceptual combinations problem’ of cognitive psychology, explaining the observed deviations from classical (Boolean, fuzzy set and Kolmogorovian) structures in terms of genuine quantum effects. In particular, natural concepts ‘interfere’ when they combine to form more complex conceptual entities, and they also exhibit a ‘quantum-type context-dependence’, which are responsible of the ‘over- and under-extension’ that are systematically observed in experiments on membership judgments.