In a earlier work [1, 2, 3, 4] we have put forward the hypothesis that two layers of thought can be identified in the human thought process, which we have called the ‘classical logical ’ layer and the ‘quantum conceptual ’ layer. In the classical logical layer thought processes are given form by an underlying Boolean logical conceptual process, its non deterministic ‘lack of knowledge ’ version modeled by Kolmogorovian probability and in an idealized form by a stochastic process. In the quantum conceptual layer, the thought process gets form under the influence of the totality of the surrounding conceptual landscape. The key event within this layer is that different concepts figure as individual entities, even when they are combinations of other concepts. A phenomenon of conceptual emergence is taking place in the quantum conceptual layer mathematically described by superposition within the quantum formalism used to model this layer. The quantum conceptual thought process is indeterministic in essence; i.e. there is not necessarily an underlying deterministic process. It is however an equally well structured layer than the classical logical one, and we belief that it is mainly the lack of insight about the structure of this quantum conceptual layer that often leads to the idea that the thought processes described in it are mainly unstructured and correspond to intuitive or irrational thought. In the present paper we analyze more in detail the cognitive and mathematical structures of these two layers of thought. More specifically we put forward a concrete
In a earlier work [1, 2, 3, 4] we have put forward the hypothesis that two layers of thought can be identified in the human thought process, which we have called the ‘classical logical ’ layer and the ‘quantum conceptual ’ layer. In the classical logical layer thought processes are given form by an underlying Boolean logical conceptual process, its non deterministic ‘lack of knowledge ’ version modeled by Kolmogorovian probability and in an idealized form by a stochastic process. In the quantum conceptual layer, the thought process gets form under the influence of the totality of the surrounding conceptual landscape. The key event within this layer is that different concepts figure as individual entities, even when they are combinations of other concepts. A phenomenon of conceptual emergence is taking place in the quantum conceptual layer mathematically described by superposition within the quantum formalism used to model this layer. The quantum conceptual thought process is indeterministic in essence; i.e. there is not necessarily an underlying deterministic process. It is however an equally well structured layer than the classical logical one, and we belief that it is mainly the lack of insight about the structure of this quantum conceptual layer that often leads to the idea that the thought processes described in it are mainly unstructured and correspond to intuitive or irrational thought. In the present paper we analyze more in detail the cognitive and mathematical structures of these two layers of thought. More specifically we put forward a concrete
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.
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.
The representation and processing of concepts is one of the hardest challenges in cognitive science. While computer scientists and engineers have focused on developing advances for particular tasks, philosophers and cognitive scientists have focused on elucidating the structural nature of meaning. A remarkable bridge between these two limited-success approaches can be found in behavioral research, since, in a variety of tasks, humans process information at a conceptual level in a way that is incompatible with classical probability and fuzzy set theory. Recently, attempts have been made to use mathematical schemes founded on quantum structures as alternative approaches. For this reason, the application of quantum structures to this type of phenomena has received increasing attention. The quantum approach allows to faithfully model a number of non-classical deviations observed in experimental data. Moreover, it shows that genuine quantum theoretical notions, such as contextuality, superposition, emergence, and entanglement, are powerful epistemic tools to understand and represent cognitive phenomena. In this thesis, we identify the limitations of classical theories to handle some important cognitive tasks, and introduce the fundamentals of the quantum cognitive approach to concepts. Next, we perform a mathematical analysis of current concept combination models and develop an extension that allows for concrete representations of multiple exemplars simultaneously. Our analysis indicates that a superposition of logical reasoning and a specific form of non-logical reasoning, where non-logical reasoning is dominant, allows to faithfully represent the experimental data. Therefore, the non-logical reasoning introduced by this model represents an important but unexplored form of reasoning in humans. In addition, we develop novel experimental methodologies to identify quantum conceptual structures for concept combinations in the context of natural language processing and psychological experiments. Namely, we present a methodology to build entangled concepts represented as sets of words with respect to a corpus of text, and present a computational and psychological methodology to discern if a collection of concepts behaves statistically as a collection of quantum or classical particles. Using both methodologies we have identified a significant presence of quantum conceptual structure in the context of natural language processing and psychological experiments.
The broader scope of our investigations is the search for the way in which concepts and their combinations carry and influence meaning and what this implies for human thought. More specifically, we examine the use of the mathematical formalism of quantum mechanics as a modeling instrument and propose a general mathematical modeling scheme for the combinations of concepts. We point out that quantum mechanical principles, such as superposition and interference, are at the origin of specific effects in cognition related to concept combinations, such as the guppy effect and the overextension and underextension of membership weights of items. We work out a concrete quantum mechanical model for a large set of experimental data of membership weights with overextension and underextension of items with respect to the conjunction and disjunction of pairs of concepts, and show that no classical model is possible for these data. We put forward an explanation by linking the presence of quantum aspects that model concept combinations to the basic process of concept formation. We investigate the implications of our quantum modeling scheme for the structure of human thought, and show the presence of a two-layer structure consisting of a classical logical layer and a quantum conceptual layer. We consider connections between our findings and phenomena such as the disjunction effect and the conjunction fallacy in decision theory, violations of the sure thing principle, and the Allais and Elsberg paradoxes in economics.
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.