Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Cambridge University Press eBooks

Quantum-inspired models of concept combinations

Jerome R. Busemeyer, Peter Bruza

Published Jul 26, 2012• 1 citation
Publisher

Abstract

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.”

DOI
10.1017/cbo9780511997716.006

Related papers

Quantum-like non-separability of concept combinations, emergent associates and abduction

Peter Bruza, Kirsty Kitto, Brentyn J. Ramm +3 more

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.

Logic Journal of IGPL•Jan 12, 2011•41 citations

Non-compositional concepts and quantum tests

Kirsty Kitto, Peter Bruza

Compositionality is a frequently made assumption in linguistics, and yet many human subjects reveal highly non-compositional word associations when confronted with novel concept combinations.This article will show how a non-compositional account of concept combinations can be supplied by modelling them as interacting quantum systems.

AIP conference proceedings•Jan 1, 2012•0 citations

Tests and Models of Non-compositional Concepts

Kirsty Kitto, Peter Bruza

The question of under what conditions conceptual representation is compositional remains debatable within cognitive science.This paper proposes a well developed mathematical apparatus for a probabilistic representation of concepts, drawing upon methods developed in quantum theory to propose a formal test that can determine whether a specific conceptual combination is compositional, or not.This test examines a joint probability distribution modeling the combination, asking whether or not it is factorizable.Empirical studies indicate that some combinations should be considered non-compositionally.

Science & Engineering Faculty•Jan 1, 2012•1 citation

Analyzing the Non-compositionality of Conceptual Combinations

Swati Singh

Objectives: This research is first of its kind to investigate the application of quantum mechanics and related mathematical models to cognitive science, specifically focusing on the challenge of modeling how the human mind assigns meaning to combinations of words. The primary objective is to classify whether given word combinations are compositional or non-compositional. Methods: The author introduces the "WWW method," which leverages the World Wide Web (WWW) as an experimental tool in place of human subjects, which makes this method cheaper and handy in comparison to the earlier methods which used human subjects for spoken and sign language studies and robots as non-human subjects. The "WWW method" involves checking the adherence to Bell inequalities and marginal selectivity. The term "meaning bound" is introduced to quantify the extent to which two words influence each other's meaning within a combination. This concept proves instrumental in devising a method for assessing compositionality using the WWW method. Findings: When the WWW serves as the information space, the verification of whether a word combination adheres to Bell inequalities entails determining if the meaning bound for the word combination (AB & C) exceeds that of its constituent parts (A & C, B & C) within the conceptual combination AB. Marginal selectivity is evaluated by establishing a vector model for grammatically framed word combinations, utilizing the WWW to collect data. If the word combination 'A then B' yields an equivalent number of hits as 'B then A,' it signifies that the word combination AB satisfies marginal selectivity. Novelty: Consequently, this research presents an accessible approach to identifying entangled pairs of word combinations using the WWW method, eliminating the need for human subject experiments. The earlier studies which include human subjects are costly and cannot be replicated anytime-anywhere, for obvious reasons. Keywords: Quantum cognition, Marginal selectivity, Compositionality, WWW method, CHSH inequality

Indian Journal of Science and Technology•Jun 25, 2024•0 citations

Quantum Structure in Cognition: Fundamentals and Applications

Diederik Aerts, Liane M. Gabora, Sandro Sozzo +1 more

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.

arXiv:1104.3344•Apr 17, 2011•17 citations

Toward a quantum theory of cognition : history, development, and perspectives

Tomás Veloz

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.

•Jan 1, 2015•3 citations
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.”
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.
The question of under what conditions conceptual representation is compositional remains debatable within cognitive science.This paper proposes a well developed mathematical apparatus for a probabilistic representation of concepts, drawing upon methods developed in quantum theory to propose a formal test that can determine whether a specific conceptual combination is compositional, or not.This test examines a joint probability distribution modeling the combination, asking whether or not it is factorizable.Empirical studies indicate that some combinations should be considered non-compositionally.
Objectives: This research is first of its kind to investigate the application of quantum mechanics and related mathematical models to cognitive science, specifically focusing on the challenge of modeling how the human mind assigns meaning to combinations of words. The primary objective is to classify whether given word combinations are compositional or non-compositional. Methods: The author introduces the "WWW method," which leverages the World Wide Web (WWW) as an experimental tool in place of human subjects, which makes this method cheaper and handy in comparison to the earlier methods which used human subjects for spoken and sign language studies and robots as non-human subjects. The "WWW method" involves checking the adherence to Bell inequalities and marginal selectivity. The term "meaning bound" is introduced to quantify the extent to which two words influence each other's meaning within a combination. This concept proves instrumental in devising a method for assessing compositionality using the WWW method. Findings: When the WWW serves as the information space, the verification of whether a word combination adheres to Bell inequalities entails determining if the meaning bound for the word combination (AB & C) exceeds that of its constituent parts (A & C, B & C) within the conceptual combination AB. Marginal selectivity is evaluated by establishing a vector model for grammatically framed word combinations, utilizing the WWW to collect data. If the word combination 'A then B' yields an equivalent number of hits as 'B then A,' it signifies that the word combination AB satisfies marginal selectivity. Novelty: Consequently, this research presents an accessible approach to identifying entangled pairs of word combinations using the WWW method, eliminating the need for human subject experiments. The earlier studies which include human subjects are costly and cannot be replicated anytime-anywhere, for obvious reasons. Keywords: Quantum cognition, Marginal selectivity, Compositionality, WWW method, CHSH inequality
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.
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.