Consider the concept combination ‘pet human’. In word association experiments, human subjects produce the associate ‘slave’ in relation to this combination. The striking aspect of this associate is that it is not produced as an associate of ‘pet’, or ‘human’ in isolation. In other words, the associate ‘slave’ seems to be emergent. Such emergent associations sometimes have a creative character and cognitive science is largely silent about how we produce them. Departing from a dimensional model of human conceptual space, this article will explore concept combinations, and will argue that emergent associations are a result of abductive reasoning within conceptual space, that is, below the symbolic level of cognition. A tensor-based approach is used to model concept combinations allowing such combinations to be formalized as interacting quantum systems. Free association norm data is used to motivate the underlying basis of the conceptual space. It is shown by analogy how some concept combinations may behave like quantum-entangled (non-separable) particles. Two methods of analysis were presented for empirically validating the presence of non-separable concept combinations in human cognition. One method is based on quantum theory and another based on comparing a joint (true theoretic) probability distribution with another distribution based on a separability assumption using a chi-square goodness-of-fit test. Although these methods were inconclusive in relation to an empirical study of bi-ambiguous concept combinations, avenues for further refinement of these methods are identified.
Consider the concept combination ‘pet human’. In word association experiments, human subjects produce the associate ‘slave’ in relation to this combination. The striking aspect of this associate is that it is not produced as an associate of ‘pet’, or ‘human’ in isolation. In other words, the associate ‘slave’ seems to be emergent. Such emergent associations sometimes have a creative character and cognitive science is largely silent about how we produce them. Departing from a dimensional model of human conceptual space, this article will explore concept combinations, and will argue that emergent associations are a result of abductive reasoning within conceptual space, that is, below the symbolic level of cognition. A tensor-based approach is used to model concept combinations allowing such combinations to be formalized as interacting quantum systems. Free association norm data is used to motivate the underlying basis of the conceptual space. It is shown by analogy how some concept combinations may behave like quantum-entangled (non-separable) particles. Two methods of analysis were presented for empirically validating the presence of non-separable concept combinations in human cognition. One method is based on quantum theory and another based on comparing a joint (true theoretic) probability distribution with another distribution based on a separability assumption using a chi-square goodness-of-fit test. Although these methods were inconclusive in relation to an empirical study of bi-ambiguous concept combinations, avenues for further refinement of these methods are identified.
Consider the concept combination “pet human.” In word association experiments, human subjects often produce the associate “slave” in relation to this combination. The striking aspect of this associate is that it is not produced as an associate of “pet” or “human” in isolation. In other words, the associate “slave” cannot be recovered from the constituent concepts. Such examples have been used in both cognitive science and philosophy to argue that concept combinations have a non-compositional semantics. This chapter will feature how various non-compositional accounts of concept combinations can be provided from quantum theory. Quantum theory is a theory which caters for the modelling of non-compositionality because the state of a quantum entangled system cannot be constructed from the states of its individual subsystems. Utilizing probabilistic methods developed for analyzing composite systems in quantum theory, we show that it is possible to classify concept combinations as having “classically compositional,” “pseudo-classically non-compositional,” or “non-classically non-compositional” semantics by determining whether the joint probability distribution modelling the combination is factorizable or not. Concept combinations and cognition The principle of semantic compositionality states the meaning of a (syntactically complex) whole is a function only of the meanings of its (syntactic) parts together with the manner in which these parts were combined (Pelletier, 1994). Whether the semantics of concepts are compositional, or not, has been somewhat of a battleground. On the one hand, there are authors like Fodor (1994) who are adamant that concepts are, and must be, compositional, but this position stands in contrast with the computational linguist Zadrozny (1994), who produced a theorem suggesting that: “the standard definition of compositionality is formally vacuous.”
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.
This article introduces a “pseudo classical” notion of modelling non-separability. This form of non-separability can be viewed as lying between separability and quantum-like non-separability. Non-separability is formalized in terms of the non-factorizabilty of the underlying joint probability distribution. A decision criterium for determining the non-factorizability of the joint distribution is related to determining the rank of a matrix as well as another approach based on the chi-square-goodness-of-fit test. This pseudo-classical notion of non-separability is discussed in terms of quantum games and concept combinations in human cognition.
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.
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.