3,174 research outputs found
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
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.Comment: 25 pages. arXiv admin note: text overlap with arXiv:1412.870
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.Comment: 31 pages, 5 figure
Eigenlogic: a Quantum View for Multiple-Valued and Fuzzy Systems
We propose a matrix model for two- and many-valued logic using families of
observables in Hilbert space, the eigenvalues give the truth values of logical
propositions where the atomic input proposition cases are represented by the
respective eigenvectors. For binary logic using the truth values {0,1} logical
observables are pairwise commuting projectors. For the truth values {+1,-1} the
operator system is formally equivalent to that of a composite spin 1/2 system,
the logical observables being isometries belonging to the Pauli group. Also in
this approach fuzzy logic arises naturally when considering non-eigenvectors.
The fuzzy membership function is obtained by the quantum mean value of the
logical projector observable and turns out to be a probability measure in
agreement with recent quantum cognition models. The analogy of many-valued
logic with quantum angular momentum is then established. Logical observables
for three-value logic are formulated as functions of the Lz observable of the
orbital angular momentum l=1. The representative 3-valued 2-argument logical
observables for the Min and Max connectives are explicitly obtained.Comment: 11 pages, 2 table
A model of the emergence and evolution of integrated worldviews
It \ud
is proposed that the ability of humans to flourish in diverse \ud
environments and evolve complex cultures reflects the following two \ud
underlying cognitive transitions. The transition from the \ud
coarse-grained associative memory of Homo habilis to the \ud
fine-grained memory of Homo erectus enabled limited \ud
representational redescription of perceptually similar episodes, \ud
abstraction, and analytic thought, the last of which is modeled as \ud
the formation of states and of lattices of properties and contexts \ud
for concepts. The transition to the modern mind of Homo \ud
sapiens is proposed to have resulted from onset of the capacity to \ud
spontaneously and temporarily shift to an associative mode of thought \ud
conducive to interaction amongst seemingly disparate concepts, \ud
modeled as the forging of conjunctions resulting in states of \ud
entanglement. The fruits of associative thought became ingredients \ud
for analytic thought, and vice versa. The ratio of \ud
associative pathways to concepts surpassed a percolation threshold \ud
resulting in the emergence of a self-modifying, integrated internal \ud
model of the world, or worldview
Quantum Theory and Conceptuality: Matter, Stories, Semantics and Space-Time
We elaborate the new interpretation of quantum theory that we recently
proposed, according to which quantum particles are considered conceptual
entities mediating between pieces of ordinary matter which are considered to
act as memory structures for them. Our aim is to identify what is the
equivalent for the human cognitive realm of what physical space-time is for the
realm of quantum particles and ordinary matter. For this purpose, we identify
the notion of 'story' as the equivalent within the human cognitive realm of
what ordinary matter is in the physical quantum realm, and analyze the role
played by the logical connectives of disjunction and conjunction with respect
to the notion of locality. Similarly to what we have done in earlier
investigations on this new quantum interpretation, we use the specific
cognitive environment of the World-Wide Web to elucidate the comparisons we
make between the human cognitive realm and the physical quantum realm.Comment: 14 page
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 (1) the measurement
process, and (2) 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
observable form as an 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
- …