66 research outputs found
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.Comment: 44 pages. arXiv admin note: text overlap with arXiv:1406.235
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.Comment: 14 pages. arXiv admin note: substantial text overlap with
arXiv:1503.0426
On the Classical-Quantum Relation of Constants of Motion
Groenewold-Van Hove theorem suggest that is not always possible to transform classical observables into quantum observables (a process known as quantization) in a way that, for all Hamiltonians, the constants of motion are preserved. The latter is a strong shortcoming for the ultimate goal of quantization, as one would expect that the notion of “constants of motion” is independent of the chosen physical scheme. It has been recently developed an approach to quantization that instead of mapping every classical observable into a quantum observable, it focuses on mapping the constants of motion themselves. In this article we will discuss the relations between classical and quantum theory under the light of this new form of quantization. In particular, we will examine the mapping of a class of operators that generalizes angular momentum where quantization satisfies the usual desirable properties.AMS subject classifications. 68Q25, 68R10, 68U0
Modeling Meaning Associated with Documental Entities: Introducing the Brussels Quantum Approach
We show that the Brussels operational-realistic approach to quantum physics
and quantum cognition offers a fundamental strategy for modeling the meaning
associated with collections of documental entities. To do so, we take the World
Wide Web as a paradigmatic example and emphasize the importance of
distinguishing the Web, made of printed documents, from a more abstract meaning
entity, which we call the Quantum Web, or QWeb, where the former is considered
to be the collection of traces that can be left by the latter, in specific
measurements, similarly to how a non-spatial quantum entity, like an electron,
can leave localized traces of impact on a detection screen. The double-slit
experiment is extensively used to illustrate the rationale of the modeling,
which is guided by how physicists constructed quantum theory to describe the
behavior of the microscopic entities. We also emphasize that the superposition
principle and the associated interference effects are not sufficient to model
all experimental probabilistic data, like those obtained by counting the
relative number of documents containing certain words and co-occurrences of
words. For this, additional effects, like context effects, must also be taken
into consideration.Comment: 27 pages, 6 figures, Late
The Complexity–Stability Debate, Chemical Organization Theory, and the Identification of Non-classical Structures in Ecology
We present a novel approach to represent ecological systems using reaction networks, and show how a particular framework called chemical organization theory (COT) sheds new light on the longstanding complexity–stability debate. Namely, COT provides a novel conceptual landscape plenty of analytic tools to explore the interplay between structure and stability of ecological systems. Given a large set of species and their interactions, COT identifies, in a computationally feasible way, each and every sub-collection of species that is closed and self-maintaining. These sub-collections, called organizations, correspond to the groups of species that can survive together (co-exist) in the long-term. Thus, the set of organizations contains all the stable regimes that can possibly happen in the dynamics of the ecological system. From here, we propose to conceive the notion of stability from the properties of the organizations, and thus apply the vast knowledge on the stability of reaction networks to the complexity–stability debate. As an example of the potential of COT to introduce new mathematical tools, we show that the set of organizations can be equipped with suitable joint and meet operators, and that for certain ecological systems the organizational structure is a non-boolean lattice, providing in this way an unexpected connection between logico-algebraic structures, popular in the foundations of quantum theory, and ecology. © 2019, Springer Nature B.V.Indexación: Scopu
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.Comment: 11 pages, no figure
- …